Chapter 13: Electrical Systems (Summary Sheet)

Part A · Circuits, charge and current

1 What Makes a Circuit

Four jobs must be done in any circuit: supply the energy (cell, battery, power supply), control the flow (switch), carry the charge (metal wires), and convert the electrical energy (load — bulb, motor, heater, buzzer).
Metals conduct electricity because some of their electrons are free to move. Conductors let charge pass easily; insulators, such as the plastic sleeving around a wire, block it.

Type of circuit	Electric current	What you observe
Closed circuit	Electric current flows through the whole circuit	Bulb glows, motor turns, buzzer sounds
Open circuit	Electric current does not flow anywhere in the circuit — not even far from the break	Nothing happens, even with a fresh battery

Exam tip: never write that the current is “used up”. Charge is not consumed — energy is transferred. If a lamp does not light, work along the loop and find the single break.

2 Circuit Diagrams: the Components and Where They Go

Circuit diagrams use standard symbols joined by straight lines. The drawing shows how the parts are connected, not how they are laid out on the bench.

Component	Job in the circuit	How it is connected, and why
Cell or battery	Supplies the energy that sets charge moving	The source of the circuit; its two terminals feed the two ends of the loop
Switch	Starts or stops the current	Closed completes the loop; open breaks it everywhere at once
Lamp	Converts electrical energy into light (and heat)	Anywhere in the loop; brightness shows the current through it
Fixed resistor	Limits the current to a steady value	In series with the part it protects or controls
Variable resistor	Changes resistance, so the current can be adjusted	In series; sliding the contact changes how much resistance is in the circuit
Ammeter	Measures the current through a component	In series with that component — the same current must pass through the meter. Low resistance; + terminal to the + side of the supply; never connected straight across the supply
Voltmeter	Measures the potential difference across a component or the source	In parallel with the part being measured. High resistance, so almost no current is taken from the circuit

Exam tip: a voltmeter connected in series, or an ammeter in parallel, gives a meaningless reading — and the ammeter can be damaged, because its resistance is very low.

3 Electric Current, the Ampere and Q = I t

Electric current is the rate of flow of electric charge past a point in a circuit.
The SI unit of current is the ampere (A): one ampere is one coulomb passing a point each second, so 1 A = 1 C/s.

Quantity	Symbol	SI unit	Meaning of the unit
Charge	Q	coulomb (C)	The base unit of charge
Current	I	ampere (A)	1 A = 1 coulomb per second
Time	t	second (s)	The base unit of time

Charge, current and time are linked by Q = I × t, which rearranges to I = Q / t. Keep Q in coulombs, I in amperes and t in seconds.
Example: a motor draws a steady 0.40 A for 2.5 minutes. t = 2.5 × 60 = 150 s, so Q = 0.40 × 150 = 60 C.
Conventional current runs from the positive terminal, round the circuit, back to the negative terminal — the direction every circuit diagram and calculation uses. The electrons in the wire actually drift the other way.

Exam tip: convert minutes to seconds and milliamperes to amperes before substituting — that single step is where most marks are lost. (The “mAh” figure on a phone battery is a charge in disguise: 1 mAh = 3.6 C.)

Part B · Driving charge: e.m.f., potential difference and resistance

4 e.m.f. and Potential Difference Compared

The electromotive force (e.m.f.) of a source is the energy it supplies per unit charge in driving that charge once round the circuit: chemical, light or mechanical energy → electrical energy.
The potential difference (p.d.) across a component is the energy that component converts per unit charge passing through it: electrical energy → other forms.
Both are energy per charge, so both are measured in volts (V): 1 V = 1 J/C. e.m.f. belongs to the source alone; p.d. belongs to a component.

	e.m.f.	Potential difference
Where it applies	The source: cell, battery, power supply	A component: bulb, resistor, motor
Energy change	Other forms → electrical	Electrical → other forms
What it describes	Energy handed to the charge	Energy taken from the charge
How it is measured	Voltmeter in parallel with the source	Voltmeter in parallel with the component
Unit	volt (V) = J/C	volt (V) = J/C

Cells in series add up: four 2.0 V cells give 8.0 V. Cells in parallel give the same voltage as one cell but share the load, so the supply lasts longer.
In one loop, every joule handed over by the source is used up by the components before the charge returns — so the e.m.f. equals the sum of the p.d.s across the components. Energy is conserved.

Exam tip: say clearly which quantity you mean — a source supplies energy per coulomb (e.m.f.), a component converts it (p.d.). Writing “the battery has a p.d. of 6 V” can cost a mark even when the number is right.

5 Resistance and the Ohm

Resistance is a measure of how strongly a component restricts the current flowing through it. Its SI unit is the ohm (Ω): one ohm is the resistance of a component in which a p.d. of one volt drives a current of one ampere, so 1 Ω = 1 V/A.
Resistance links the p.d. across a component to the current through it: V = I × R, rearranged as R = V / I.
For a given p.d. the relationship runs both ways: a larger resistance means a smaller current, and a smaller resistance lets a larger current through.
Size and shape matter: a long thin wire has high resistance, a short thick wire has low resistance. A variable resistor works by changing how much wire is in the circuit.

6 Change One Thing and the Others Follow

The current through a component depends on both the p.d. across it and its own resistance. Never assume a current stays the same when the circuit is changed.

What you change	What happens to the current	Why
Increase the p.d. across a fixed resistor	The current increases	Each coulomb is given more energy, so charge is driven round faster
Increase the resistance at fixed p.d.	The current decreases	The component restricts the flow more strongly (I = V / R)
Add a resistor in series	The current falls; every component now gets less p.d.	Resistances in series add, so the total resistance is larger than the biggest single value
Add a resistor in parallel	The current from the source rises; each branch still gets the full p.d.	An extra route lowers the combined resistance to less than the smallest branch resistance
Adjust a variable resistor	The current can be set to any value in range	The resistance is changed deliberately, and the current follows

Investigate the effect of varying resistance on the current

Step	What you do	What you read, and why
Set up	Join a cell, a switch, the resistor under test and an ammeter in series in one loop	The ammeter must be in series so the same current passes through it
Keep the same	Use the same source and the same wires throughout; change only the resistance	A fair test: the p.d. driving the charge does not change, so any change in the current comes from the resistance
Change the resistance	Swap fixed resistors of different values, or slide the variable resistor so more of its wire is in the circuit	Each change puts a different resistance in the path of the charge
Read and record	Note the ammeter reading for each resistance, with the switch closed	Pair each resistance with the current it gives
The result	The current is smaller for a larger resistance, and larger for a smaller resistance	At the same p.d., current and resistance pull in opposite directions — the trend is all that is required here

Part C · Series and parallel circuits

7 Two Ways to Join Components

There are only two arrangements to know. A circuit that shares its potential difference between components is a series circuit; one that supplies the full potential difference to each branch is a parallel circuit. Everything else in this table follows from that one fact.

Quantity	Series	Parallel
Routes for charge	One loop only: every charge passes through every component	One route per branch; charge divides at each junction
Current	I = I₁ = I₂ = I₃ — the same at every point of the loop	I = I₁ + I₂ + I₃ — charge is conserved at the junction, so what leaves the source must return to it
Potential difference	V = V₁ + V₂ + V₃ — the source's total is shared out, and the largest resistance takes the largest share	V = V₁ = V₂ = V₃ — every branch is connected straight across the source, so each gets the full value
Effective resistance	R = R₁ + R₂ + R₃ — the values add, so R is larger than any single component	1/R = 1/R₁ + 1/R₂ + 1/R₃ — so R comes out smaller than the smallest branch, and the smaller branch resistance carries the larger current

8 Why Household Wiring is Parallel

Mains wiring in a building is parallel throughout, with each socket or lighting point on its own branch and its own switch.
Each appliance therefore gets the full mains p.d., so appliances are made to one standard voltage; each can be switched independently, since a switch in one branch does not affect the others; and a fault in one branch does not stop the rest.
The price of the design: every extra branch lowers the combined resistance and raises the total current drawn, which is why the supply cables warm up.
That is the reason for fuses, circuit breakers and correctly chosen wire thickness — and the reason overloading a socket with too many appliances is dangerous.

Part D · Power, energy and the cost of electricity

9 Electrical Power

Power is the rate at which electrical energy is transferred or converted into other forms: P = E / t, where E is the energy converted and t the time taken.
The SI unit of power is the watt (W), and one watt is one joule per second (1 W = 1 J/s). A high-power appliance converts a large amount of energy every second.
Power also links the p.d. across a component to the current through it: P = V × I. Our air fryer is labelled 230 V, 1250 W, so it draws I = P / V = 1250 / 230 = 5.4 A.
The rating on a label tells you the rate of energy conversion, not the resistance directly.

Exam tip: the watt is a rate, not an amount of energy. An appliance's power says nothing about how much energy it uses until you know how long it runs.

10 Energy in Joules and in Kilowatt-hours

Energy converted is found from E = P × t, and the unit follows the units you feed in.

Route	Power unit	Time unit	Energy unit
Small amounts	watt (W)	second (s)	joule (J)
Household amounts	kilowatt (kW)	hour (h)	kilowatt-hour (kWh)

One kilowatt-hour is 1000 W running for 3600 s: 1 kWh = 3 600 000 J. It is simply a larger, more convenient energy unit — the one electricity is charged in.
Example: the 1250 W air fryer used for 45 minutes takes 1.25 kW × 0.75 h = 0.9375 kWh, which is 3 375 000 J.
Keep the two routes separate: watts with seconds give joules; kilowatts with hours give kilowatt-hours.

11 The Cost of Electricity

A bill is a charge for energy, not for power: the supplier states a tariff in dollars per kilowatt-hour, the meter records the total energy used, and cost = energy in kWh × tariff.
Four items in one home, over 30 days at $0.28 per kWh:

Appliance	Power (W)	Daily use (h)	Energy per month (kWh)	Cost per month ($)
Air fryer	1250	0.75	28.13	7.88
Rice cooker	650	0.75	14.63	4.10
Dehumidifier	320	6.00	57.60	16.13
LED desk lamp	9	4.00	1.08	0.30
Total	—	—	101.43	28.40

Notice the dehumidifier: the lowest power of the three large items, yet the highest cost — because it runs for six hours a day. Cost depends on power and time.

Exam tip: watch the units. Watts to kilowatts is a division by 1000, minutes to hours a division by 60, and the tariff must be per kWh — not per MJ. Given joules with a $/kWh tariff, divide by 3 600 000 first.

Part E · Effects, hazards and safety

12 Three Effects of an Electric Current

A current does not only light lamps: charge passing through a device can produce heating, a magnetic field or a chemical change.

Effect	What happens	Applications
Heating	Charge does work against the resistance of the wire, so electrical energy becomes thermal energy inside it	Kettle, iron, toaster, hair dryer, and the filament lamp, which glows because it is hot
Magnetic	A current creates a magnetic field around the wire; wound round an iron core it makes an electromagnet, which can be switched on and off and can be made stronger	Doorbell, relay, loudspeaker, electric motor, magnetic crane in a scrapyard
Chemical	A current can drive chemical changes in a liquid, and can deposit one metal onto another (electroplating); a cell or battery stores chemical energy and converts it to electrical energy	Plating a cheaper metal with chrome, refining metals, recharging a battery

Heating is the whole point in a kettle element, deliberately made of high-resistance wire. Everywhere else it is wasted: the cable feeding a television warms up, and an old filament lamp gives out far more heat than light for the same brightness.

13 Electrical Hazards

Most hazards come from one change in the system: too large a current, in a wire too thin to carry it.

Hazard	How it arises	What it can cause
Overheating cables	A large current in a long, thin wire, or too many appliances on one socket	Insulation softens or melts; bare metal is exposed
Short circuit	Damaged insulation lets two wires touch, so the current takes a very low-resistance path	A very large current, sparks and fire risk
Electric shock	Touching exposed live metal, or switches and sockets with wet hands	Current through the body; can be fatal
Fire	Heat from an overloaded cable or a spark ignites nearby material	Fire spreading through the installation

Overloading follows straight from parallel wiring: each extra branch lowers the combined resistance and raises the total current, so the supply cables carry more than they were chosen for.

14 Safe Use and Using Less

Precautionary measures that make household electricity safe:

Measure	Why it helps
Fuse or circuit breaker in the circuit	Its wire melts or its switch trips when the current is too large, breaking the circuit before the cables overheat
Wire of the correct thickness	A thick wire has lower resistance, so it carries a large current without heating dangerously
Do not overload one socket	Extra branches lower the combined resistance and raise the total current beyond what the wiring can take
Keep insulation in good condition	Undamaged insulation keeps the live metal away from fingers and stops wires touching each other
Dry hands, and switch off before handling	Water conducts, so wet skin lowers the resistance of the path through the body; switching off at the socket removes the supply

Ways to reduce the consumption of electrical energy in the home: use LED bulbs instead of filament lamps (the same light for a small fraction of the energy), choose lower-power appliances, run high-power appliances for fewer hours, switch appliances off at the socket instead of leaving them on standby, compare energy labels when buying, and keep the air-conditioner near 25 °C with doors and windows shut.
Cost-cutting attacks both numbers at once — lower power and fewer hours.

Part F · Exam Tips from the Syllabus Pointers

15 Exam Tips: What Each Syllabus Pointer Asks For

The MOE pointer	What earns the mark
Current, potential difference and resistance, with SI units	Name the quantity, then its unit: ampere (A), volt (V), ohm (Ω). A number without a unit can lose the mark on its own.
Draw and interpret circuit diagrams; set up circuits	Use standard symbols in one unbroken loop; ammeter in series, voltmeter in parallel. Check the loop is closed before explaining anything.
Investigate how series and parallel arrangements affect the current	Classify the circuit first, then say what happens to the current and why: resistances add in series, so the amount of current decreases; an extra branch (parallel) lowers the combined resistance, so the amount of current increases.
Investigate the effect of varying resistance, with fixed or variable resistors	Describe the fair test — same source, one resistance changed at a time, ammeter in series — and report the trend: the amount of current decreases as resistance increases. The formula is not required.
Describe the effects of a current, and their applications	Name the effect and give one application: heating → kettle element; magnetic → electromagnet, relay or motor; chemical → electroplating or a cell.
State how changes cause hazards, and the precautions	Pair each hazard with its measure: overloaded socket or thin wire → fuse, circuit breaker or correct wire thickness; damaged insulation → replace it; wet hands at a switch → dry hands and switch off first.
Explain power and state its SI unit	Power is a rate: the watt is one joule per second. A “230 V, 1250 W” label means 1250 J converted every second, not 1250 J used.
Calculate the cost of using appliances in kilowatt-hours	Convert to kilowatts and hours first, then cost = energy in kWh × tariff. State that the longest-running appliance can cost the most even at low power.
Show awareness of reducing electricity use at home	Name the change and the saving: LED bulbs, lower-power appliances, fewer hours, switching off at the socket instead of standby.