Grade 10 Electricity Study Notes

Welcome to Fundamentals of Electricity

Electricity is the invisible energy that lights our homes, charges our phones, runs hospitals and powers the factories around us. In this strand you start from the basics — what electricity is and why we depend on it — and build up to designing your own circuits.

What this strand covers

• Introduction to Electricity — its importance, careers, safety rules, and the people responsible for safety.
• D.C Electric Circuits — circuit parts, symbols, Ohm's Law, series and parallel networks, power and energy, fault-finding.
• Cells and Batteries — how cells work, charging, discharging, maintenance and safe disposal.
• Capacitors and Capacitance — components that store charge in nearly every electronic device.
• Pictorial Drawing — drawing electrical components in 3D so others can build them.

How to approach this strand

Move from simple to complex. Each sub-strand builds on the one before. Pay close attention to safety — that habit must stay with you in every practical task.

Lesson 1 focus

This first sub-strand, Introduction to Electricity, is mostly about why we study electricity. You will look at how it supports daily life, the careers it offers, the safety rules that keep workers alive, and the people who make sure electrical work is done safely.

What this lesson covers

This lesson follows your course book's four sections:

1. Importance of electricity in the society — how electricity supports daily life, industry, healthcare, transport and more.
2. Career opportunities in the field of electricity — eight careers you could pursue after school.
3. Safety regulations while carrying out electrical tasks — the rules and equipment that prevent shock, burns and fire.
4. Role of stakeholders in application of electrical safety — what workers, employers and the government each do to keep electrical work safe.

By the end you should be able to explain why electricity matters, name several careers, list the main workshop safety rules, identify each piece of PPE on sight, and describe each stakeholder's role.

Importance of electricity in the society

What is electricity?

Electricity is a form of energy that comes from the flow of electric charge through a conductor such as a wire. You meet it the moment you switch on a light, charge a phone, or boil water in a kettle.

Electricity is special because it can be moved easily along wires, then changed into other forms of energy — heat in a cooker, light in a bulb, sound in a radio, motion in a fan. That is why nearly every modern appliance is designed to run on it.

Electricity in cooking

Electricity powers electric stoves, microwaves and ovens, making cooking faster, safer and cleaner than firewood or charcoal.

Compared to a charcoal jiko, an electric cooker:

• Heats up almost instantly.
• Produces no smoke, so the kitchen stays clean.
• Has a controllable temperature, so food rarely burns.

Electricity in lighting

Electricity lights homes, schools, streets and workplaces. This lets people work and move safely even at night. Street lighting also reduces accidents and crime by removing dark spots.

Electricity in household appliances

Many home tools rely on electricity, including washing machines, iron boxes and air conditioners. Without it these jobs would have to be done by hand and would take much longer.

Electricity in communication and entertainment

Electricity powers televisions, radios and phones, keeping people informed, entertained and connected. Even the phone networks themselves run on electricity — every mast, base station and data centre needs continuous power.

Electricity in food preservation

Fridges and freezers use electricity to keep food cold. This prevents spoilage and reduces food wastage. Without refrigeration, milk, meat and many vegetables would have to be eaten the same day they are bought.

Electricity in education

Schools depend on electricity to run computers, projectors and the internet. This makes digital learning possible — videos, online lessons, and research from many sources.

Electricity in transport

Electric vehicles use stored electrical energy instead of petrol or diesel. They produce no exhaust fumes while being driven, so they are an eco-friendly alternative.

Electricity also runs traffic lights, railway signals and petrol-station pumps — parts of transport we don't always notice.

Electricity in industries

Factories use electricity to run heavy machinery and production lines. Without it, the manufacture of cement, sugar, soap and vehicles would stop. Electricity also powers the lighting, ventilation and computer systems that keep modern factories running.

A production line is a row of machines, each doing one step of making a product, with a conveyor belt moving the product between them. Every part of the line runs on electricity.

Electricity in hospitals

Hospitals depend on electricity for life-saving equipment — operating-theatre lights, ventilators, X-ray machines, and incubators for new-born babies.

An incubator is a clear plastic box that keeps a premature baby warm at a steady temperature. Both the heater and the air pump run on electricity, so the box must never lose power.

Vaccines and medicines are also stored in refrigerators that must stay cold at all times. A loss of power can directly threaten lives, which is why hospitals also keep backup generators. Hospitals and factories are two of the most important essential services any country has — healthcare keeps people alive and manufacturing keeps the economy running, and both stop the moment electricity stops.

Career opportunities in the field of electricity

Overview of careers in the field of electricity

The field of electricity offers many careers — from hands-on work in homes and factories, to designing the power systems of whole cities, to running a power station.

The eight main careers are:

1. Electrical technician
2. Electrical engineer
3. Electronics technician
4. Power plant operator
5. Industrial electrician
6. Renewable energy technician
7. Control systems technician
8. Field service engineer

Each needs a different mix of skills and qualifications, and each is in real demand in Kenya.

Electrical technician

An electrical technician installs, maintains and repairs electrical systems in homes, businesses and industries.

This is the person who comes to your house to fix a faulty socket or wire up a new building. Most technicians work hands-on, with insulated tools and PPE.

Electrical engineer

An electrical engineer designs and develops electrical systems such as circuits, power generation systems and distribution networks.

If a new town is being built, the engineer plans where the power lines will go, what voltage they will carry, and how electricity will reach every house. Engineers usually study at university and work mostly with calculations and drawings before any wiring is installed.

Electronics technician

An electronics technician works with electronic devices, repairing and testing components like circuits, sensors and microchips.

Where an electrical technician deals with the wiring of a building, an electronics technician deals with what is inside a device — the small green circuit board you would find in a TV, radio or phone.

Power plant operator

A power plant operator manages and runs the equipment that generates electricity, keeping power production safe and efficient.

This person works inside a power station — where electricity is produced before being sent through the national grid. Their day is spent watching control screens, adjusting settings, and reacting quickly when readings move outside safe ranges.

Industrial electrician

An industrial electrician installs and maintains electrical systems in factories, including machinery and control systems.

This is similar to an electrical technician, but focused on factory settings — large motors, conveyor belts, and the heavy power supplies that drive them. The voltages and currents are much higher than at home, so industrial electricians need extra training.

Renewable energy technician

A renewable energy technician works with solar, wind and hydroelectric power systems, installing and maintaining them.

In Kenya, much of this work involves solar panels — fitting them on rooftops, connecting them to batteries, and keeping them working over the years. As more homes and farms switch to clean energy, this career is growing fast.

Control systems technician

A control systems technician works with automated systems that manage industrial equipment and processes.

An automated system is one that runs by itself once it has been set up — for example, a bottling plant where bottles fill, cap and label themselves while one technician watches a screen. The control systems technician keeps that automation working: programming the controllers, fixing faults, and tuning performance.

Field service engineer

A field service engineer travels to different locations to install, maintain or repair electrical and electronic systems.

"In the field" simply means "out at the customer's site" rather than in a workshop. A medical-equipment company in Nairobi, for example, might send a field service engineer to a hospital in Kisumu when an X-ray machine breaks down.

As you read these eight careers, notice which ones match your own interests — someone who enjoys hands-on repair fits the technician roles, while someone who enjoys planning and calculation fits the engineer role.

Project: The career wheel

A career wheel is a simple visual tool — a rotating disc divided into sections, each labelled with a different career. Spinning the wheel gives a quick way to discuss any one career at random. Many of these careers are in high demand in Kenya — electrical technology is a viable and respected career path.

Materials needed

• Cardboard or stiff paper
• Coloured markers or crayons
• A ruler, scissors, glue or tape
• Magazine cut-outs or printed pictures of electrical careers
• A split pin for the centre

Steps

1. Cut a large circle from the cardboard.
2. Use a ruler to divide the circle into eight equal sections.
3. Write the name of one career inside each section, with a small picture.
4. Use a split pin at the centre to attach a pointer that can spin freely.
5. Display the finished wheel to the class and explain each career in your own words.
6. Take turns spinning the wheel and discussing each career as the pointer lands on it.

Safety regulations while carrying out electrical tasks

The ten core safety rules

Electricity can cause electric shock, burns and fires. Every electrical workshop follows a set of safety rules. Each rule exists because someone, somewhere, has been hurt or killed by ignoring it — together they form the system that keeps electrical workshops safe.

1. Use tools and equipment according to the manufacturer's instructions.
2. Use insulated tools and cables to prevent shock from contact with live parts.
3. Wear appropriate Personal Protective Equipment (PPE) — insulated gloves, rubber-soled shoes and safety glasses.
4. Do not overload sockets or extension cords.
5. Carry out routine checks on equipment, cables and outlets, by qualified personnel only.
6. Earth the metallic parts of equipment by connecting them to the earth terminal.
7. Only qualified electricians should install, maintain or repair electrical systems.
8. Keep fire extinguishers and first-aid kits readily available.
9. Keep cables away from water, and do not run them under rugs or furniture.
10. Mark electrical hazards clearly, and label high-voltage areas.

Insulated tools and cables

Insulation is a non-conducting layer — usually rubber or thick plastic — that wraps around the metal part of a tool or wire. It stops electric current from passing through into anything it touches.

Electricians use insulated tools such as screwdrivers and pliers, with thick plastic-covered handles. They also use insulated cables, where the metal wire is wrapped in coloured plastic.

If a bare metal handle touches a live wire, current flows straight into the user's hand. An insulated handle blocks that path.

PPE: Insulated gloves

Insulated gloves are thick rubber gloves worn by electricians to block current from passing into the hands when handling live parts.

They are heavier and looser than ordinary gloves, usually orange or red so they are easy to spot. Each pair carries a voltage rating — the electrician picks gloves rated higher than the voltage being worked on. Before each use, inspect the gloves for cuts, cracks or pinholes — even a tiny hole lets current through, and damaged gloves must be replaced, not repaired.

PPE: Rubber-soled shoes

Rubber-soled shoes are work shoes whose soles are made of rubber, which does not conduct electricity. They break the path that current would otherwise take through the body to the ground.

For a shock to happen, current usually needs a complete path from the live wire, through the body, into the ground. Rubber soles cut that path right at the floor.

PPE: Safety glasses

Safety glasses are clear protective eyewear worn during electrical work. They protect the eyes from sparks, flying debris and arc flashes.

An arc flash is a sudden burst of light and heat that can happen if a tool short-circuits live wires. Without safety glasses, an arc flash can permanently damage the eyes. The same principle applies at home and at school — never poke metal objects into sockets, and never open up an appliance while it is plugged in.

Spotting unsafe practice: the overloaded socket

One of the easiest ways to spot a dangerous installation is to look for an overloaded socket — a single wall outlet powering many appliances through a tangle of plugs and extension cords.

Every wall socket is rated for a fixed amount of current. Drawing more than that — by stacking extension strips and plugging in many appliances at once — causes the wires to overheat. Overheated wires are a leading cause of house fires. This is rule 4 from the safety list being broken.

Marking electrical hazards

Rule 10 says electrical hazards must be clearly marked, and high-voltage areas must be properly labelled. The most common warning sign is the yellow triangle with a black lightning bolt — a worldwide warning that there is dangerous voltage on the other side.

These signs work as a silent guard: even when no one is around, the sign tells you to keep away or take extra care.

Role of stakeholders in application of electrical safety

The three stakeholders

Electrical safety is not the job of one person. Three groups — workers, employers and government agencies — each carry their own responsibilities. The system works only when all three play their part.

Think of it as three layers of protection. The government sets the rules. The employer applies them in the workplace and equips the worker. The worker follows them on the job. If any layer fails, accidents follow.

Workers

Workers are the people who actually carry out electrical tasks. Their responsibilities are to:

1. Follow safety guidelines when operating equipment.
2. Use PPE to protect themselves from hazards.
3. Notify supervisors about faults, damaged equipment or unsafe conditions.
4. Use tools properly, according to the manufacturer's instructions.
5. Undergo proper training on safe work and emergency procedures.

Even a fully equipped workplace becomes unsafe the moment a worker decides to skip the rules.

Employers

Employers are the people or companies who hire workers. Their responsibilities are to:

1. Make sure equipment is safe, well-maintained and inspected regularly.
2. Provide safety training to workers.
3. Enforce safety protocols such as maintenance schedules and emergency response plans.
4. Ensure the workplace complies with safety regulations.
5. Provide workers with proper PPE and tools.

An employer who skips training, hides faulty equipment, or fails to provide PPE creates an unsafe workplace — even when the workers are willing to follow the rules.

Government agencies

Government agencies are the bodies set up by the state to oversee safety in workplaces across the country. Their responsibilities are to:

1. Set electrical safety standards and regulations.
2. Ensure compliance with safety laws.
3. Conduct routine inspections of workplaces.
4. Offer training programmes and safety guidelines to employers and workers.
5. Impose penalties and fines on employers who fail to comply.

In practice, an inspector visits a workplace, checks compliance against the standards, and issues a notice or fine if rules are broken — this is how a written rule turns into action on the ground. Without government oversight, employers, workers and the wider public would have no clear set of rules to follow, and no consequence for breaking them — government regulations protect everyone, not just those at work.

Key Points

• Electricity is a form of energy that powers homes, schools, industries, hospitals, transport and communication.
• The field offers eight main careers: electrical technician, electrical engineer, electronics technician, power plant operator, industrial electrician, renewable energy technician, control systems technician and field service engineer.
• Ten core safety rules govern the electrical workshop — covering manufacturer's instructions, insulation, PPE, overload, routine checks, earthing, qualified personnel, emergency equipment, water, and clear marking of hazards.
• PPE — insulated gloves, rubber-soled shoes and safety glasses — is the worker's last line of defence.
• Safety is shared among three stakeholders: workers follow the rules, employers apply them, and the government sets and enforces them.

Stakeholder responsibilities at a glance

What this lesson covers

An electric circuit is a closed path that lets current flow. In this sub-strand you will learn how to build, analyse and troubleshoot circuits powered by direct current (DC) — the kind of current produced by a battery.

This lesson follows your course book's nine sections:

1. Properties of an electric circuit — the parts a circuit must have to work.
2. Zeroing of measuring instruments — making sure ammeters and voltmeters read accurately.
3. Analysis of DC circuits using applicable laws — Ohm's Law and Kirchhoff's laws.
4. Constructing resistor networks — combining resistors in series and parallel.
5. Power and energy in DC circuits — calculating P = VI and E = VIt.
6. Faults in DC circuits — open circuits, short circuits and other common faults.
7. Differences between conductors, insulators and semiconductors — three families of electrical materials.
8. Mechanism of electrical conduction in metals — why metals conduct.
9. Applications of DC circuits — where DC is used in daily life.

By the end you should be able to draw circuits using standard symbols, calculate currents, voltages and resistances, identify faults, and explain why metals conduct electricity while plastics do not.

Properties of an electric circuit

What is an electric circuit?

An electric circuit is a closed path made up of electrical components, through which current flows from a source to a load and back to the source.

Its main job is to transfer electrical energy from the source (like a battery) to the load (like a bulb), where the energy is changed into another form — light, heat, sound or motion.

Every electric circuit has four major parts:

1. Source of power — provides electrical energy.
2. Connecting cables — carry the current from one part to the next.
3. Load — converts electrical energy to a useful form.
4. Control element — regulates the flow of current.

If even one of these is missing or broken, the circuit will not work.

Source of power

The source of power is the part of a circuit that provides electrical energy. Without a source, there is nothing to push the current around the circuit.

Common sources include dry cells, batteries, and the wall socket from the mains supply. In DC circuits at this level, the source is usually one or more dry cells (1.5 V each).

Connecting two or more cells together gives a higher voltage — three 1.5 V cells in series give 4.5 V, enough to make a bulb glow more brightly than a single cell could.

Connecting cables

Connecting cables link all the parts of a circuit so electrical energy can flow from one part to the next. They are the "roads" of the circuit.

The metal inside is usually copper, because copper is an excellent conductor and is widely available. The metal is wrapped in a coloured plastic layer for insulation — to stop current escaping or causing shock when touched.

Load

A load is a part of the circuit that converts electrical energy into another useful form of energy. Without a load, energy from the source has nothing useful to do.

Examples of loads:

• A lamp — converts electrical energy to light (and some heat).
• A resistor — converts electrical energy to heat.
• A motor — converts electrical energy to motion.
• A radio speaker — converts electrical energy to sound.

Control element

A control element is the part of the circuit that regulates the flow of current — letting the user decide when current flows and when it does not. The most common control element is a switch.

When a switch is closed, current flows and the circuit works. When the switch is open, the path is broken and no current flows. A wall light switch is a control element you use every day.

Standard electrical symbols

Drawing each component as a picture would be slow and unclear. Instead, every part of a circuit has a standard symbol that any electrician anywhere in the world recognises.

The four most important symbols at this level are:

• A conducting wire — drawn as a plain straight line.
• A switch — drawn as a small lever next to a gap in the line.
• A lamp — drawn as a circle with a cross inside it.
• A cell (source of electricity) — drawn as a long thin line beside a short thick line, with the long line as the positive terminal and the short line as the negative terminal.

A circuit drawn with these symbols is called a circuit diagram.

Zeroing of measuring instruments

What zeroing is and why it matters

Zeroing is the process of setting the scale of a measuring instrument to read exactly zero when nothing is being measured.

Take an ammeter. Before it is connected to a circuit, no current flows through it, so the pointer should sit exactly on the "0" mark. If the pointer rests slightly above or below zero, every reading the ammeter takes will be off by that same amount — this is called a zero error.

Zeroing matters because it removes this hidden offset. Without zeroing, every reading is wrong, even when the meter looks like it's working fine.

Positive and negative zero error

There are two types of zero error:

• Positive zero error — the pointer rests above zero (e.g. at 0.3 A) when it should read zero. The meter then reads too high by that amount.
• Negative zero error — the pointer rests below zero (e.g. at -0.2 A) when it should read zero. The meter then reads too low by that amount.

Either way, the fix is the same — adjust the pointer back to zero before taking a reading.

How to zero an ammeter

Most analogue ammeters and voltmeters have a small zero-adjustment screw on the front or side. Adjusting this screw moves the pointer until it sits on the zero mark.

Steps

1. Place the ammeter on a flat surface so it stays steady.
2. Make sure it is not connected to any circuit (no current flowing).
3. Locate the zero-adjustment screw on the meter face.
4. Insert a small screwdriver into the slot.
5. Gently rotate the screw until the pointer lines up exactly with the zero mark.

Once zeroed, the meter is ready to give accurate readings.

Analysis of DC circuits using applicable laws

Ohm's Law

Ohm's Law is the most important rule in this whole sub-strand. It states that the current flowing between two points in a circuit is directly proportional to the voltage across the two points, provided temperature stays the same.

The law is written as:

V = I × R

Where:

• V = voltage across the two points, measured in volts (V).
• I = current flowing between the points, measured in amperes (A).
• R = resistance between the two points, measured in ohms (Ω).

Two important consequences follow:

• If resistance increases (with voltage held constant), the current decreases.
• If voltage increases (with resistance held constant), the current increases.

Worked example using V = IR

A simple circuit has a 6 V battery connected across a resistor of 3 Ω. Calculate the current flowing in the circuit.

Solution

Using Ohm's Law:

V = I × R

Rearranging to make I the subject:

I = V ÷ R

I = 6 ÷ 3

I = 2 A

So a current of 2 amperes flows in the circuit.

Notice the steps: write the formula, rearrange to find what you need, substitute the numbers, and give the answer with its unit.

Current and voltage in a series circuit

A series circuit connects components one after another, so there is only one path for the current to take.

Two important rules apply to series circuits:

• The current is the same at every point in the circuit.
• The sum of the voltage drops across all the loads is equal to the source voltage.

The second rule is called Kirchhoff's Voltage Law (KVL):

V = V₁ + V₂ + V₃

Where V is the source voltage, and V₁, V₂, V₃ are the voltage drops across each load. The higher the resistance of a component, the larger its share of the voltage drop.

Current and voltage in a parallel circuit

A parallel circuit connects components side by side, so each one has its own separate path back to the source.

Two important rules apply to parallel circuits:

• The voltage across every branch is the same as the source voltage.
• The total current from the source is the sum of the branch currents.

The second rule is called Kirchhoff's Current Law (KCL):

I = I₁ + I₂ + I₃

Where I is the total current and I₁, I₂, I₃ are the currents through each branch. KCL is sometimes stated as: "the total current flowing into a junction equals the total current flowing out of it."

Constructing resistor networks

Resistors in series — total resistance

When resistors are connected in series, the total resistance is the sum of the individual resistances:

R_T = R₁ + R₂ + R₃ + … + R_N

This makes sense — adding more resistors in line just adds more "obstacles" for the current to fight through.

Worked example — resistors in series

Calculate the total resistance of four resistors connected in series with values 12 Ω, 8 Ω, 7 Ω and 13 Ω.

Solution

For series resistors:

R_T = R₁ + R₂ + R₃ + R₄

R_T = 12 + 8 + 7 + 13

R_T = 40 Ω

So the four resistors together act like one resistor of 40 ohms.

Resistors in parallel — total resistance

When resistors are connected in parallel, the total resistance is found using:

1/R_T = 1/R₁ + 1/R₂ + 1/R₃

Notice that adding more resistors in parallel decreases the total resistance — the opposite of series. Each new branch gives the current another path to take, so the overall opposition drops.

The total resistance of a parallel combination is always smaller than the smallest individual resistor in the group.

Worked example — resistors in parallel

Calculate the total resistance of three resistors of 40 Ω, 20 Ω and 40 Ω connected in parallel.

Solution

Using the parallel formula:

1/R_T = 1/R₁ + 1/R₂ + 1/R₃

1/R_T = 1/40 + 1/20 + 1/40

Find a common denominator (40):

1/R_T = 1/40 + 2/40 + 1/40 = 4/40

1/R_T = 1/10

R_T = 10 Ω

Notice that the answer (10 Ω) is smaller than the smallest individual resistor (20 Ω) — exactly as the rule predicts.

Two resistors in parallel — shortcut formula

For exactly two resistors in parallel, there is a quick shortcut:

R_T = (R₁ × R₂) ÷ (R₁ + R₂)

This is sometimes called the "product over sum" formula. It only works for two resistors at a time — for three or more, use the longer formula above.

Quick example

For two parallel resistors of 6 Ω and 12 Ω:

R_T = (6 × 12) ÷ (6 + 12) = 72 ÷ 18 = 4 Ω

Same answer as the long method, but faster.

Power and energy in DC circuits

Power in a DC circuit

Electrical power is the rate at which a circuit uses electrical energy. It is measured in watts (W).

For a DC circuit:

P = V × I

Where:

• P = power in watts (W).
• V = voltage in volts (V).
• I = current in amperes (A).

A 6 V bulb drawing 0.5 A is using P = 6 × 0.5 = 3 watts of power. The higher the wattage, the more energy the device uses every second.

Energy in a DC circuit

Electrical energy is the total amount of electrical work done over a period of time. It is measured in joules (J).

For a DC circuit:

E = V × I × t

Where:

• E = energy in joules (J).
• V = voltage in volts (V).
• I = current in amperes (A).
• t = time the current flows, in seconds (s).

Since P = V × I, this can also be written as E = P × t — energy equals power multiplied by time. A 100 W bulb left on for 60 seconds uses 100 × 60 = 6 000 joules.

Worked example — combined circuit

A 12 V battery powers a circuit with a 6 Ω resistor in parallel with a series combination of an 8 Ω and a 4 Ω resistor. Find the total resistance, the total current, the power supplied, and the energy used in 20 seconds.

Solution

Step 1 — Total resistance.
The 8 Ω and 4 Ω resistors are in series, so their combined resistance is 8 + 4 = 12 Ω.
This 12 Ω branch is in parallel with the 6 Ω resistor:
1/R_T = 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4
R_T = 4 Ω

Step 2 — Total current.
I = V ÷ R_T = 12 ÷ 4 = 3 A

Step 3 — Power supplied.
P = V × I = 12 × 3 = 36 W

Step 4 — Energy used in 20 seconds.
E = P × t = 36 × 20 = 720 J

So in 20 seconds, the circuit uses 720 joules of electrical energy.

Faults in DC circuits

Open circuit

An open circuit is a circuit where the current cannot flow because the path is broken somewhere. The break could be a snapped wire, a switch left in the "off" position, or a loose terminal.

Symptoms of an open circuit:

• The bulb or load does not work.
• The ammeter reads zero — no current is flowing.
• A voltmeter across the break still reads the source voltage, because the supply is still pushing.

Short circuit

A short circuit happens when current finds an unintended path of very low resistance, usually bypassing the load. Without the load to limit the current, the current rises sharply.

Symptoms and dangers:

• The current is very high — far higher than normal.
• Wires can overheat and melt.
• If unchecked, a short circuit can cause fires or destroy components.
• This is why circuits are protected by fuses or circuit breakers, which cut off the current before damage occurs.

Dry joints and loose connections

Two more common faults are easy to miss because the circuit looks fine.

• A dry joint is a poorly soldered point — the solder hardened before it bonded properly. The joint looks connected but the metal underneath is barely touching, so current passes through unreliably.
• A loose connection is a wire or component that has not been tightened down at its terminal. The wire can wobble in and out of contact.

Both cause the same symptoms: the circuit works sometimes, the load flickers, and gentle tapping can change the behaviour. These intermittent faults are especially common in old radios and home wiring.

Troubleshooting with a multimeter

A multimeter is a single instrument that can measure voltage, current and resistance. It is the main tool for finding faults in DC circuits.

To find a fault:

1. Switch off the circuit and disconnect the source.
2. Set the multimeter to the resistance (Ω) setting.
3. Touch the two probes to the ends of the section being tested:
   • A reading of "0 Ω" or near zero — the section is connected (good).
   • A reading of "infinite" or "OL" (overload) — the section is broken (open circuit).
4. Move along the circuit until you find the broken section.

Differences between conductors, insulators and semiconductors

Three types of electrical materials

All electrical materials fall into three groups, based on how easily they let current flow.

• Conductors — let current flow easily. Examples: copper, aluminium, silver.
• Insulators — do not let current flow. Examples: plastic, rubber.
• Semiconductors — fall in between. They conduct better than insulators but worse than conductors. Examples: silicon, germanium.

Each group has its own use. Copper carries current inside cables (conductor). Plastic wraps the outside to keep current in (insulator). Silicon is used inside diodes, transistors and microchips (semiconductor) — the electronics you will study in Strand 4.

Mechanism of electrical conduction in metals

Why metals conduct: the sea of free electrons

Metals conduct electricity because of their special atomic structure. In a metal, each atom releases some of its outer electrons, which are then free to move anywhere through the metal.

This creates two parts:

• A fixed lattice of positively charged metal ions (the atoms minus their lost electrons).
• A "sea" of free, delocalised electrons drifting between the ions.

When the metal is connected to a battery, the battery's voltage pushes the free electrons from the negative terminal, through the metal, towards the positive terminal. For every electron that leaves at one end, a new one enters at the other end. This continuous drift of free electrons is the electric current.

Insulators have no free electrons — their electrons are tightly held by their atoms — so current cannot flow through them.

Applications of DC circuits

Where DC circuits are used in daily life

DC circuits are everywhere in modern life because they give a steady, constant power supply — exactly what most electronic devices need.

Common applications:

• Smartphones, laptops and digital cameras — run on DC from rechargeable batteries.
• Electric vehicles — use DC from on-board batteries to drive the motor.
• Telecommunication systems — DC powers signal amplifiers and processors in both wired and wireless networks.
• Medical monitoring equipment — heart-rate monitors, oxygen sensors and many diagnostic tools all run on DC.
• Solar power systems — solar panels produce DC, which is stored in batteries before use.

Wherever a battery is involved, a DC circuit is at work.

Key Points

• Every electric circuit needs four parts: a source, connecting cables, a load, and a control element.
• Standard circuit symbols let any electrician anywhere read a diagram instantly.
• Zeroing a measuring instrument removes hidden offset errors before measurement.
• Ohm's Law: V = IR — the foundation of all DC circuit calculations.
• Series circuits: same current everywhere, voltages add up (KVL), R_T = R₁ + R₂ + R₃.
• Parallel circuits: same voltage on every branch, currents add up (KCL), 1/R_T = 1/R₁ + 1/R₂ + 1/R₃.
• Power: P = VI (in watts). Energy: E = VIt (in joules).
• Common faults: open circuit, short circuit, dry joint, loose connection — all found with a multimeter.
• Three families of materials: conductors (copper), insulators (plastic), semiconductors (silicon).
• Metals conduct because they have a "sea of free electrons" that can drift through the lattice.

Series vs parallel — a side-by-side comparison

A cell and a battery

A cell is a single unit that produces electricity from a chemical reaction.

A battery is two or more cells joined together to give more electrical energy than one cell alone.

The 1.5 V dry cell in a wall clock is one cell. The 12 V box under a car bonnet is several cells joined together — a battery.

Primary cells and secondary cells

Cells fall into two families:

• Primary cells — used once, then thrown away. The chemical reaction inside cannot be reversed. Examples: AA and AAA dry cells in remotes, wall clocks and torches.
• Secondary cells — can be recharged and reused many times. The reaction is reversed by passing electricity back into the cell. Examples: phone, laptop and car batteries.

What a simple cell needs

A simple cell is the most basic working cell you can build. It needs three things:

• Two electrodes made from different metals (commonly zinc and copper)
• An electrolyte — a liquid that lets ions move (an acid, an alkali, a salt solution, or even a fruit like a lemon or orange)
• A conducting wire linking the electrodes outside the electrolyte

Push a clean strip of zinc and a clean strip of copper into a lemon, connect a voltmeter across them, and the meter shows a small voltage. You have built a primary cell.

Which electrode is positive, which is negative

The two metals do not behave the same way in the electrolyte. The metal higher up in the reactivity series releases electrons more readily.

In a zinc–copper simple cell, zinc is more reactive than copper, so:

• Zinc loses electrons → becomes the negative electrode (cathode). Electrons leave the zinc through the wire.
• Copper receives the electrons → becomes the positive electrode (anode).

While the wire is connected, electrons flow through the wire from zinc to copper. That flow of electrons is the current the voltmeter detects.

Defect 1: Polarisation

Leave a simple cell connected for a few minutes and the voltmeter reading slowly drops — even though the lemon and the metals are still there. The first reason is polarisation.

When the cell delivers current, a layer of hydrogen bubbles forms on the copper plate. This layer:

• Coats the copper electrode, blocking the electrolyte from reaching the metal
• Increases the internal resistance of the cell
• Makes the current fall to a very small value quickly

Remedy: add potassium dichromate to the cell. It reacts with the hydrogen bubbles and clears them off the copper plate, so the cell keeps working.

Defect 2: Local action

If the zinc is impure (containing tiny bits of iron, lead or other metals), small unwanted reactions happen on the surface of the zinc itself — even when the cell is not connected. This is local action.

The result: the zinc is eaten away gradually, the cell makes less current over time, and it has a short useful life.

Three ways to reduce local action

• Use pure zinc — impurities like iron and lead start the unwanted reactions, so highly purified zinc minimises the problem.
• Amalgamate the zinc — coat the zinc with mercury. The smooth amalgam layer stops impurities from contacting the electrolyte.
• Use inhibitors — chemical additives in modern cells suppress the unwanted side reactions.

Why this matters: polarisation and local action are why your school-lab "simple cell" can never replace a real dry cell in a torch. Real commercial cells are designed to avoid both — and managing these defects is exactly what gives a commercial cell a useful life of months instead of minutes.

What happens during discharging

A secondary cell can be recharged and reused. Phone, laptop, motorcycle and car batteries are all secondary cells.

When a secondary cell is discharging (in normal use):

• The stored chemical energy is converted into electrical energy.
• Electrons flow out of the cell's negative terminal, through the external load (a bulb, a phone, a motor), and back to the positive terminal.
• Chemical reactions at the two electrodes drive that electron flow.
• The cell's voltage gradually drops as it runs — that is why your phone shows a falling battery percentage.

What happens during charging

When the cell goes flat, you connect it to an external voltage source stronger than the cell — a phone charger, a battery charger. This forces current backwards through the cell.

• The chemical reactions that happened during discharge now run in reverse.
• The direction of electron flow inside the cell reverses compared with discharging.
• The by-products of discharge are converted back into the original reactants.
• The cell's voltage rises as it charges.
• Once full, the cell can be disconnected and used again.

Lab demonstration — charge and discharge

In the lab, two clean lead plates sit in dilute sulphuric (VI) acid. Two switches let you choose what the cell does:

• Close S₁ — the cell connects to the charging battery. Current flows in; the cell charges. The ammeter shows a positive reading.
• Open S₁ and close S₂ — the (now charged) cell connects to a load. Current flows the other way through the ammeter, driving the load — the cell is discharging.

The same cell drives the meter in both directions, depending on which switch is closed. That reversal is the whole point of a secondary cell.

The key difference between primary and secondary cells: in a primary cell, the chemical reaction is one-way — it ends when the reactants are used up. In a secondary cell, the reaction is two-way — what was used up during discharge is rebuilt during charging.

Series connection — voltages add

To connect cells in series, join the positive terminal of one cell to the negative terminal of the next, and so on along the line. The two end terminals (one positive, one negative) become the terminals of the whole battery.

Total voltage = sum of all the individual cell voltages.

Three 1.5 V cells in series give 1.5 + 1.5 + 1.5 = 4.5 V across the ends. The same current flows through every cell — there is only one path for it to take.

Where you see this every day: the three or four AA cells in a TV remote sit end to end inside the battery compartment — a series array. Whenever you need a higher voltage than one cell can give, you stack cells in series.

Parallel connection — voltage stays, current capacity grows

To connect cells in parallel, join all the positive terminals together and all the negative terminals together. The whole bunch then has just two terminals — one common positive and one common negative.

Total voltage = the voltage of one single cell. Adding more cells in parallel does not raise the voltage.

Three 1.5 V cells in parallel still give 1.5 V across the combination. So why bother? Because parallel gives electrons more paths to flow — the battery can deliver more current, and it lasts longer before going flat.

Where you see this every day: big solar power systems use parallel-connected batteries to store enough energy to run a household for hours. Power banks that "hold more charge" usually have several cells in parallel inside the case. Whenever you need more current or longer running time — but not more voltage — you go parallel.

Series vs parallel — side-by-side

The two arrangements solve different problems. Series gives you more voltage. Parallel gives you more current capacity and runtime.

What charging means

Charging a battery means restoring its energy by reversing the chemical reactions that happened during discharge. Different battery types react differently to charging — the wrong method can ruin a battery, overheat it, or even cause it to leak or burst. There are five common methods, each suited to different battery chemistries and uses.

Method 1 — Constant current charging

A fixed current is supplied to the battery. As the battery charges, its voltage rises gradually.

Used for nickel-cadmium (Ni-Cd) and nickel-metal-hydride (NiMH) batteries.

Method 2 — Constant voltage charging

A fixed voltage is applied across the battery terminals. As the battery charges, the current it draws falls gradually — the gap between the charger's voltage and the battery's voltage gets smaller.

It is simple and cheap, but must be watched to avoid overcharging. Commonly used for lead-acid batteries.

Method 3 — Constant Current / Constant Voltage (CC/CV) charging

A two-stage method that combines the first two. It starts with constant current, then switches to constant voltage when a set voltage is reached.

• Stage 1 — CC mode: the charger pushes a fixed current. Voltage rises until it hits a reference voltage (V_ref).
• Stage 2 — CV mode: the charger holds the voltage at V_ref. Current falls from the reference current (I_ref) down to a small cutoff current (I_co), and charging is complete.

Combines the safety of constant voltage with the speed of constant current. This is the standard way lithium-ion batteries (in phones and laptops) are charged.

Method 4 — Trickle charging

A very low constant current is supplied — just enough to make up for self-discharge and keep the battery full.

• Used for standby applications like emergency lighting and uninterruptible power supplies (UPS).
• Keeps batteries always ready, but long-term trickle charging can wear the battery out.

Method 5 — Smart charging

Microcontrollers watch the battery's condition and adjust both charging voltage and current as needed. Includes temperature sensing, overcharge protection and automatic cut-off.

• Used in modern smartphones and laptops.
• The safest method but also more expensive, because of the extra electronics needed.

Why your phone charger is "smart": modern phones use lithium-ion cells, which can catch fire if overcharged. The charger and the phone work together — checking voltage, current and temperature thousands of times a second — to charge fast without crossing a danger line.

Mini solar-powered charging station

You can build a small charger using a solar panel, a rechargeable battery, a diode and some wires.

The diode is essential: it lets current flow only one way — from panel to battery. Without it, when the sun goes down and the panel's voltage drops, the battery would push current back into the panel and lose its charge.

Materials for cleaning a battery

To clean a battery (typically a lead-acid car or motorcycle battery), you need four basic items:

• Baking soda
• Water
• A piece of cloth
• A corrosion inhibitor (where available)

Baking soda is the key item — it neutralises the acid corrosion that builds up on the terminals.

The cleaning process

Cleaning a battery follows a strict order. Skipping the first step can be dangerous.

1. Disconnect the battery before doing anything else.
2. Wear goggles and gloves, then mix baking soda with water to form a paste.
3. Gently scrub the terminals with the mixture — the baking soda neutralises the acid corrosion.
4. Wipe off with clean water.
5. Reconnect the battery securely.
6. Safely dispose of the waste rags and water.

Checking the electrolyte and the voltage

Three checks tell you the state of a lead-acid battery:

• Acid density is checked using an acid hydrometer. The deeper the float sinks, the weaker the acid. If it rides high, the acid is strong and the battery is well charged.
• Water level can be checked visually against the maximum and minimum level marks on the side of the battery casing.
• Battery voltage is checked with a digital multimeter set to the DC voltage range.

Doing these three checks regularly is what extends the working life of motorcycle and car batteries from a few months to several years.

Hazardous materials inside cells and batteries

Batteries contain hazardous materials. That is why throwing them in an ordinary rubbish bin is dangerous and, in many places, illegal.

Hazardous materials commonly found inside cells and batteries

• Cadmium
• Lead
• Zinc
• Manganese
• Nickel
• Silver
• Mercury
• Lithium
• Sulphuric (VI) acid

When batteries are dumped in landfills, these materials leak out into the soil and water as the casing breaks down — causing soil contamination, water contamination, and human health risks through air, water and food.

Safe handling rules

When working with cells and batteries, especially during maintenance:

• Wear gloves and goggles, plus clothing that covers the body — to minimise skin contact with acid and other chemicals.
• Charge batteries in a well-ventilated area — charging produces gases (especially hydrogen from lead-acid batteries) which can build up and become explosive.
• Store batteries in a cool, dry place — avoid extreme heat or cold, both shorten battery life and can cause leakage or rupture.
• Never throw batteries in the trash — this is the rule that pulls everything else together.

Safe disposal — recycling facilities

The most effective way to dispose of batteries safely is to take them to a recycling facility. It is wrong to throw batteries into landfills. At a recycling centre, the metals and acid are separated and reused, instead of leaking into the environment.

The citizenship link: safe battery disposal is one small action with an outsized effect. The household that takes its used batteries to a collection point — instead of dropping them in the bin — keeps local soil and water cleaner.

Key Points

Cells, batteries and the simple cell

• A cell is a single unit; a battery is two or more cells joined together.
• Primary cells cannot be recharged; secondary cells can.
• A simple cell needs two different metals (electrodes), an electrolyte, and a wire.
• The more reactive metal becomes the negative electrode; the less reactive becomes the positive.
• Polarisation (hydrogen on copper, cured by potassium dichromate) and local action (impurities eating zinc, cured by pure zinc, amalgamation, or inhibitors) are the two simple-cell defects.

Charging, discharging, and connecting cells

• Discharging turns chemical energy into electrical energy; electrons leave the negative terminal, do work in the load, and return to the positive.
• Charging reverses the chemistry by forcing current backwards into the cell.
• Series connection adds voltages; same current through every cell.
• Parallel connection keeps voltage the same but increases current capacity and runtime.

Charging methods

Maintenance and safety

• Clean terminals with baking soda and water; always disconnect the battery first.
• Check acid density with an acid hydrometer, water level visually, voltage with a multimeter.
• Hazardous materials inside batteries: cadmium, lead, zinc, manganese, nickel, silver, mercury, lithium, sulphuric (VI) acid.
• Wear gloves and goggles; charge in ventilated areas; avoid extreme temperatures.
• Never bin batteries — take them to a recycling facility.

What a capacitor is

A capacitor is an electronic component that stores electric charge in an electric field.

Inside, every capacitor has the same three parts:

• Two conductive plates — usually flat metal sheets
• A dielectric — a non-conductive (insulating) material sandwiched between the plates
• Two leads — connecting wires that come out from each plate

The capacitor stores energy in an electrostatic field that builds up between the two plates whenever a voltage is applied. The kind of dielectric used (paper, ceramic, plastic, electrolyte) determines the type of capacitor.

Where you find them: the rectifier in a phone charger has a capacitor to smooth out fluctuations. A camera flash has a big one — it stores energy, then dumps it all at once into the flash bulb.

The capacitor symbol

In a circuit diagram, a capacitor is drawn as two parallel lines separated by a small gap. The two lines stand for the plates; the gap stands for the dielectric.

How a capacitor charges

Before a voltage is applied, the capacitor is discharged — there is no charge on either plate.

When you connect the capacitor to a battery:

• Electrons accumulate on one plate — that plate becomes negatively charged.
• The other plate loses electrons — it becomes positively charged.
• An electric field builds up across the dielectric, between the two plates.
• That field is where the electrical energy is stored.

The dielectric does not let current pass through it (it is an insulator), so no current flows from one plate to the other across the dielectric. But charge piles up on the plates, and that charge is the stored energy.

Holding and releasing the charge

A charged capacitor holds its charge as long as the applied voltage is maintained. Disconnect the battery and the charge stays put — the dielectric blocks the charge from flowing across.

When the capacitor is then connected to a circuit (without the battery), the stored charge flows out, releasing the stored energy until all of it has been used up. The capacitor is now discharged again.

This is the heart of how a capacitor works: store on demand, release on demand.

Camera flash is the classic example. The flash circuit charges a big capacitor slowly from the camera battery. When you press the shutter, the capacitor dumps all its charge in a fraction of a second through the flash tube — producing a brief, very bright burst of light no battery alone could deliver that fast.

Voltage rises gradually as a capacitor charges

⚠️ Safety: capacitors should always be handled with care to avoid electric shock and fire. Always make sure they are properly discharged after use before touching the leads.

Connect a capacitor in series with a resistor to a battery, close a switch, and start a stopwatch. Read the voltage across the capacitor every 10 seconds.

The reading will start near 0 V and rise gradually towards the supply voltage, levelling off as the capacitor fills up. It does not jump straight to the full voltage — it climbs along a curved path.

Where you see this: timing circuits in alarms, automatic lights and oven timers all use this gradual rise. The circuit waits until the capacitor's voltage reaches a set level, then triggers — that is how the timer 'knows' how long to wait.

Current falls gradually as a capacitor charges

Now do the same experiment, but read the current instead of the voltage. The result is the mirror image of the voltage curve.

The current starts at its maximum value (the moment you close the switch, lots of electrons rush onto the plates), then drops smoothly to zero as the capacitor fills up. Once the capacitor is fully charged, no more current flows.

Why voltage rises while current falls

The two curves are linked. As the capacitor's voltage rises, it pushes back harder against the battery. The bigger the back-pressure from the capacitor, the smaller the current that can flow.

Eventually the capacitor's voltage equals the supply voltage. There is no longer any voltage difference to push current — and so the current drops to zero.

Where you see this: the gradual dimming of an LED that has a capacitor across it — it stays bright while the capacitor discharges, then fades smoothly to off as the current drops.

Reading the labels on a capacitor

Pick up a real capacitor and look closely. Printed on its body, you will find:

• Manufacturer's name — the company that made it
• DC working voltage — the safe operating voltage; never apply more than this
• Capacitance value — usually in microfarads (μF), nanofarads (nF) or picofarads (pF)
• Tolerance — how much the actual capacitance can vary from the printed value (e.g. ±10%)
• Temperature coefficient — for some capacitors, how much the capacitance changes with temperature

Choosing a capacitor for a job

When you pick a capacitor for a circuit, think about four things:

• Capacitance value — does it store enough charge for the job?
• Voltage rating — choose a capacitor with a higher voltage rating than the circuit's operating voltage. (For a 9 V circuit, use a capacitor rated 12 V or more.)
• Tolerance — does the application need precise capacitance (tight tolerance) or is a rough value enough?
• Temperature coefficient — will the capacitor be in a hot or cold environment? If yes, the capacitance must stay stable.

The voltage rule is the safety-critical one — exceed it and the capacitor can fail, leak, or even explode.

Matching capacitors to applications

Three quick examples from real circuits:

• A 12 V DC power supply that needs to smooth out voltage fluctuations after rectification — uses a large electrolytic capacitor (high capacitance, e.g. 1000 μF, voltage rating safely above 12 V).
• A 555 timer circuit giving a 1-second LED delay on a 5 V supply — uses a small ceramic or film capacitor whose value, together with the timing resistor, sets the delay.
• An audio amplifier that needs to block DC while letting AC audio signals pass — uses a coupling capacitor, sized so it passes the audio frequencies but blocks the steady DC.

Different jobs need different capacitor values, voltage ratings and types — there is no single capacitor that fits every circuit.

Series connection — voltages split, charge is the same

Capacitors can be combined in series or parallel to give a chosen effective capacitance.

To connect capacitors in series, join them end to end — positive of one to negative of the next, like cells in series.

When several capacitors are connected this way:

• The same charge sits on every capacitor: Q₁ = Q₂ = Q₃
• The supply voltage splits across the capacitors: V = V₁ + V₂ + V₃
• The total capacitance is smaller than any individual capacitor

Formula for total capacitance in series

For capacitors in series, the reciprocals add:

1 / C_T = 1/C₁ + 1/C₂ + 1/C₃

Solve for C_T (the total capacitance) by inverting both sides at the end.

For just two capacitors in series, there is a useful shortcut:

C_T = (C₁ × C₂) / (C₁ + C₂)

⚠️ Important: the total capacitance of capacitors in series is always smaller than the smallest capacitor in the chain.

Worked example: three capacitors in series

Three capacitors of capacitance 1.5 μF, 2 μF and 3 μF are connected in series to a supply voltage of 12 V. Find the combined capacitance and the total charge.

Combined capacitance:

1/C_T = 1/1.5 + 1/2 + 1/3 = 2/3

C_T = 0.667 μF

Total charge:

Q = C_T × V = 0.667 × 10⁻⁶ × 12 ≈ 8.0 × 10⁻⁶ C (8 μC)

Notice how the combined capacitance (0.667 μF) is smaller than the smallest individual one (1.5 μF) — exactly as the rule predicts.

The two-capacitor shortcut

When only two capacitors are in series, the formula simplifies neatly:

C_T = (C₁ × C₂) / (C₁ + C₂)

Worked example with C₁ = 10 μF and C₂ = 22 μF:

C_T = (10 × 22) / (10 + 22) = 220 / 32 ≈ 6.875 μF

Faster than the reciprocal method when there are only two capacitors.

Parallel connection — voltage same, charges add

To connect capacitors in parallel, join all the positive plates together and all the negative plates together, just like cells in parallel.

When capacitors are connected this way:

• The voltage across each capacitor is the same as the supply voltage: V = V₁ = V₂ = V₃
• The total charge is the sum of the individual charges: Q = Q₁ + Q₂ + Q₃
• The total capacitance is the sum of the individual capacitances

Formula for total capacitance in parallel

For capacitors in parallel, the capacitances simply add up:

C_T = C₁ + C₂ + C₃

Adding more capacitors in parallel always gives a bigger total capacitance — the opposite behaviour from series.

Worked example: three capacitors in parallel

Three capacitors of capacitance 4.5 μF, 2.5 μF and 3 μF are connected in parallel to a supply of 3 V. Find the total capacitance, total charge, and charge on each capacitor.

Total capacitance:

C_T = 4.5 + 2.5 + 3 = 10 μF

Total charge:

Q = C_T × V = 10 × 10⁻⁶ × 3 = 30 × 10⁻⁶ C (30 μC)

Charge on each capacitor (each sees the full 3 V):

Check: the charges on each capacitor add up to the total charge. That confirms the calculation.

Where you see this: power banks that "hold more charge" use several cells (and capacitors) in parallel inside the case. Same voltage, more total stored charge.

Solving a mixed series-parallel circuit

Real circuits often mix series and parallel together. The trick is to break the problem into parts and solve one combination at a time.

Worked example:

A 3 μF capacitor is connected in series with a parallel combination of 2 μF and 4 μF. The supply voltage is 100 V. Find the total capacitance and the total charge.

Step 1 — combine the parallel section first

The 2 μF and 4 μF are in parallel:

C_parallel = 2 + 4 = 6 μF

Step 2 — that combination is now in series with the 3 μF

1/C_T = 1/3 + 1/6 = 3/6 = 1/2

C_T = 2 μF

Step 3 — total charge

Q = C_T × V = 2 × 10⁻⁶ × 100 = 2 × 10⁻⁴ C

The general rule: simplify the parallel groups first (they add up), then combine the result in series (use reciprocals or the two-capacitor shortcut). Work from the simplest grouping outward.

Where you see this: filter circuits in radios and televisions use mixed series-parallel capacitor arrangements to pass some signals and block others.

Capacitors in motors

Capacitors are vital components in many electric motors, especially in single-phase motors. They:

• Help the motor start by giving an extra burst of current at switch-on
• Improve running efficiency
• Reduce vibration and rough running

Look inside a fan, a washing machine, or an air conditioner and you will find a "motor start capacitor" — a small barrel-shaped or rectangular component wired into the motor's start winding.

Capacitors in control circuits

Capacitors are used in control circuits for traffic lights — the gradual charging of a capacitor (the voltage-time curve from earlier) is what sets the timing of how long each colour stays on.

The same principle is used in:

• Oven and microwave timers
• Camera self-timers
• Automatic light switches with delay

In each case, the circuit waits until the capacitor's voltage hits a chosen level — and then triggers the next action.

Capacitors and power efficiency

Capacitors reduce power loss in electrical systems. By smoothing out fluctuations and correcting for phase shifts caused by motors and other inductive loads, they make electricity production and use more efficient and cost-effective.

Power factor correction capacitors are common in factories and large buildings — they save money on the electricity bill by reducing wasted power.

Key Points

What a capacitor is and how it works

• A capacitor stores electric charge in an electric field between two plates separated by a dielectric (insulator).
• The standard circuit symbol is two short parallel lines with a small gap.
• When charging, electrons gather on one plate (negative) and leave the other plate (positive). The dielectric holds the charge in place.
• The capacitor stays charged as long as the voltage is applied. When connected to a load, it releases its stored energy.

Charging characteristics

• Voltage rises along a curve, slowing as it approaches the supply voltage.
• Current falls along a mirror-image curve from maximum to zero.
• The two are linked: the bigger the voltage on the capacitor, the smaller the current that can still flow.

Selecting capacitors

• Read these labels: manufacturer's name, capacitance value, DC working voltage, tolerance.
• Always pick a voltage rating higher than the circuit's operating voltage.
• Match capacitance, type and tolerance to the job — smoothing, timing, signal coupling each need different choices.

Series and parallel formulas

Why capacitors matter

• Help motors start and run smoothly
• Set the timing in control circuits (traffic lights, oven timers)
• Reduce power loss in factories and large buildings

What pictorial drawing is

A pictorial drawing shows an object in three dimensions — height, width and depth — on a flat (two-dimensional) piece of paper. The drawing makes a flat sheet look solid.

This is different from an ordinary 2D drawing of a square or a circle. In a pictorial drawing, you can see more than one face of the object at the same time. For example, you might see the top, the front and one side all in the same picture.

Three types of pictorial drawing

There are three main types of pictorial drawing. Each one uses different rules to show the 3D shape.

• Isometric drawing — three faces visible, drawn at equal angles
• Oblique drawing — front face true to shape, sides slanting backward
• Perspective drawing — uses a vanishing point to make far things look smaller

The next three blocks unpack the rules for each.

Principles of isometric drawing

In an isometric drawing:

• The three sides of the object — front, top and one side — are all visible
• All three sides are drawn to equal lengths (no shrinking)
• The width and depth lines are drawn at 30° angles from the baseline (the horizontal)
• All three dimensions (height, width and depth) are drawn to scale, with angles of 120° between the axes
• The object appears balanced and neat in three dimensions

Principles of oblique drawing

In an oblique drawing:

• The front face is drawn as it is — true to its real shape, with no tilting
• The depth (the side that recedes into the page) is drawn at an angle of 45° from the baseline
• The front stays flat and accurate, while the sides slant backward
• The object appears to be projected backward, with the front face remaining true in shape

Principles of perspective drawing

Perspective drawing makes a flat picture look 3D by using a vanishing point. All depth lines run toward this point. Objects look smaller as they get further away — exactly how the real world looks to your eyes.

The key difference: isometric and oblique drawings keep parallel lines parallel. Perspective drawing breaks that rule deliberately to make the picture look more lifelike.

Three views: front, end and top elevations

A 3D object can be seen from many viewpoints. Three viewpoints are special:

• End elevation (EE) — also called the end view. The object as seen from the end (the side).
• Front elevation (FE) — also called the front view. The object as seen from straight in front.
• Top view — also called the plan view. The object as seen from directly above.

Each viewpoint gives a different 2D shape on paper.

Orthographic projection

When you put the front, end and top views on one drawing — flat and to scale — the result is called an orthographic projection. It is the standard way engineers communicate complete information about a 3D object.

A complete orthographic drawing usually shows:

• Front elevation (front view)
• End elevation (side view)
• Top view (plan view)

Hidden details that cannot be seen directly from a viewpoint are shown using dashed lines.

For example, a hole drilled through an object will show as a dashed circle on the top view (you can see the circle from above) but as dashed parallel lines on the front view (because the hole is hidden inside the body).

First angle vs third angle projection

There are two ways to lay out the views in an orthographic drawing — they differ only in where each view is placed on the sheet.

• First angle projection — the top view sits below the front view; the right-side view sits to the left of the front view. Common in Europe, Africa and Asia.
• Third angle projection — the top view sits above the front view; the right-side view sits to the right of the front view. Common in the USA and Canada.

Both methods give the same 2D shapes — they just arrange them differently on the page. Engineering drawings always carry a small symbol showing which projection method has been used, so anyone reading the drawing knows what to expect.

Isometric grid paper

To draw cleanly without measuring every angle, draughtsmen use special grid papers that already have the angles marked.

Isometric grid paper has lines arranged in a pattern of equilateral triangles, all meeting at 120° angles.

When you draw on isometric grid paper:

• All three axes (length, width, height) are reduced equally, giving a 3D representation where dimensions are proportional
• The 30° angles for width and depth are already drawn for you — you just follow the lines
• You can sketch isometric views without a set square

Oblique grid paper

Oblique grid paper is built on the rules of oblique projection. One face of the object is drawn parallel to the drawing plane (so it looks true to shape), and the other sides recede at 45°.

The 45° lines are already drawn on the paper, so you do not need a set square either.

About perspective: the reason perspective drawing exists is that our eyes really do see distant things smaller than near things — look down a long railway line and the rails seem to meet in the distance. That meeting point is the vanishing point. Isometric and oblique drawings ignore this effect deliberately, so the drawing stays simple to measure.

Why circles become ellipses in pictorial drawings

A circle drawn on the front face of a real object looks like a perfect circle when you see the face directly. But in an isometric or oblique drawing, that same face is tilted. A tilted circle looks like an ellipse.

In an isometric drawing, a circle on any face appears as an ellipse. To draw it accurately, we use a four-arc construction — four circular arcs joined together to make a shape that looks like a true ellipse.

Drawing an isometric circle (compass method)

To draw an isometric circle of a chosen diameter (e.g. 50 mm):

1. Using a 30°/60° set square, draw an isometric box (a rhombus) the same size as the diameter of the circle.
2. Join the corners of the box to find the centre.
3. Draw 30° lines through the centre point, parallel with the outside of the box.
4. Join the points A to B and A to C (these are the corners of the rhombus).
5. Place the compass spike at point A. Draw an arc from B to C with your compass.
6. Repeat for the opposite side, drawing a matching arc.
7. The straight lines from steps 4 and 6 have created points D and E. Place your compass spike at D and E to draw the smaller side arcs that join the large arcs into a full ellipse.

Drawing an oblique circle (four-centre method)

For an oblique circle, the method is similar but uses a parallelogram (a tilted rectangle) instead of an isometric box:

1. Draw a parallelogram PQRS of side equal to the circle's diameter (e.g. 50 mm).
2. Bisect all four sides of the parallelogram — find the midpoint of each side. Mark them a, b, c, d.
3. From each midpoint, draw a perpendicular to the side. Where these perpendiculars meet, you get four points: W, X, Y and Z — the four centres.
4. With centres W and X, draw the two large arcs of radius R.
5. With centres Y and Z, draw the two smaller arcs that complete the ellipse.

Key idea: both methods use four arcs to build the ellipse — but the construction starts from a different shape (rhombus for isometric, parallelogram for oblique).

Hidden details and the dashed-line convention

Looking at a 3D object from one direction, some parts will be hidden behind the body of the object — a hole drilled through, a groove cut into the back, a slot inside. These are called hidden details.

In a technical drawing, hidden details are shown using dashed lines. When you read the drawing, dashed lines tell you "this feature exists, but you cannot see it directly from this viewpoint."

Slanting faces

A slanting face is a face that is tilted away from the front, top or side directions. It does not appear as a true rectangle in any of the standard views — it appears as an angled line or an oddly-shaped polygon, depending on the viewpoint.

When reading a pictorial drawing, slanting faces show as straight lines that do not run horizontally or vertically — they cut across at angles. Looking at the same object from a different elevation can make a slanting face easier to see.

Side elevation (left and right)

The side elevation is the view of the object from one side. There are two of them:

• Right-side elevation — what you see standing on the right of the object, looking left
• Left-side elevation — what you see standing on the left of the object, looking right

Both sides show the depth of the object plus any features that are not visible from the front. The right-side and left-side views are mirror images of each other if the object is symmetrical, and are different if the object has features only on one side.

Rear elevation

The rear elevation is the view from the back of the object. It is used to show features on the back — for example, doors, windows, or pipe connections — that are not visible from the front.

Together, the front, rear, two side and top views form the six standard orthographic views. Most engineering drawings only use three (front, side, top) — but when an object has features on more sides, additional views are added.

Fundamental principles of isometric projection

Pulling everything together, these are the fundamental principles of isometric projection:

1. The three axes (length, width, height) are all drawn at 120 degrees to each other.
2. Lines parallel to the isometric axes are drawn to their true lengths — so you can measure straight off the drawing.
3. Circles appear as ellipses in isometric projections. They are built from four arcs.
4. Isometric projections do not use perspective. Objects do not appear smaller with distance — they keep their true size on the page.

The box method and non-isometric lines

For complex objects, draughtsmen use the box method.

• First, enclose the object inside an isometric box of the right overall size.
• Then draw the object's features inside the box, working from corners and known points.

Lines that are not parallel to the isometric axes are called non-isometric lines. These lines:

• Are not drawn to their true lengths (they appear shorter or longer depending on the angle)
• Need special construction techniques — usually you locate their endpoints from known measurements, then connect those endpoints

Advantages of isometric projections

Isometric projections have three big strengths:

• Ease of construction — relatively easy to build, no complex perspective calculations needed
• Clear representation — give a clear, understandable view of 3D objects
• Measurement accuracy — true lengths along the isometric axes allow accurate measurements directly off the drawing

Disadvantages of isometric projections

Two main weaknesses:

• The lack of perspective can make objects appear distorted, especially large objects
• They do not show how objects really look to the human eye — the picture is technically correct but feels "wrong" to look at, compared to a perspective drawing

For this reason, architects often use perspective drawings for client presentations (more lifelike), and switch to isometric or orthographic for the actual building plans (easier to measure).

Why pictorial drawings matter in engineering design

Pictorial drawings matter because they:

• Enhance visualisation — give a "real-world" view of the object, making the overall shape, form and how parts fit together easier to understand
• Help with assembly and manufacturing — used in assembly instructions and manufacturing documents to show how parts fit together
• Are common in technical drawings, engineering diagrams and architectural plans
• Are used in video games and computer graphics to create 3D-like environments

Without pictorial drawing, an engineer in one country could not communicate a design to a manufacturer in another country with any confidence that they would build the same thing.

Key Points

Three types of pictorial drawing

From 3D to 2D — orthographic projection

• Three standard views: front elevation, end elevation, top (plan) view.
• Two layout standards: first angle (top below front) and third angle (top above front).
• Hidden details are shown using dashed lines.

Grid papers

• Isometric grid: equilateral triangles at 120° — for isometric drawings.
• Oblique grid: squares plus 45° diagonals — for oblique drawings.

Drawing circles in pictorial views

• A circle on a tilted face appears as an ellipse.
• Both isometric and oblique circles are constructed from four arcs.
• Isometric uses a rhombus as the construction box; oblique uses a parallelogram.

Reading a drawing

• Dashed lines = hidden details.
• Slanting faces appear as angled lines, neither horizontal nor vertical.
• Side and rear elevations show features not visible from the front.

Strengths and weaknesses

• Isometric advantages: easy to construct, clear representation, true measurements along axes.
• Isometric disadvantages: no perspective — large objects can look distorted; not lifelike.