Electrical Systems is about how electric charge is made to flow through a circuit in a controlled path, and how that flow is measured, controlled and used safely. The topic starts with the two requirements for a current to flow and the standard circuit symbols. It then covers current, potential difference and resistance, series and parallel circuits, the three effects of an electric current, electrical power and the electricity bill, and electrical safety at home.
These ideas are reused all the way to Sec 3/4 D.C. circuits and practical electricity. Almost every calculation in the topic is built from current, potential difference and resistance and the formula linking them. Setting out each calculation as formula, substitution, then answer with unit earns marks at every step.
What these notes cover
- •What makes a circuit work
- •Circuit symbols you must know
- •Current, potential difference and resistance
- •Resistance of a wire and controlling current with resistors
- •Series vs parallel circuits
- •Why homes are wired in parallel
- •Three effects of an electric current
- •Electrical power and energy
- •The kilowatt-hour and your electricity bill
- •Household electrical hazards
- •Fuses, switches, earth wires and circuit breakers
- •Common mistakes and exam technique
Key definitions
- Electric current
- The rate of flow of charge, which is the amount of charge passing a point in the circuit per second. Measured in amperes (A) with an ammeter connected in series.
- Potential difference (p.d.)
- What drives the current through a component, also called voltage. Measured in volts (V) with a voltmeter connected in parallel across the component.
- Resistance
- The opposition of a component to the flow of current through it. Measured in ohms (Ω).
- Power
- The rate at which an appliance converts electrical energy into other forms of energy. Measured in watts (W), where 1 W = 1 J/s.
- Kilowatt-hour (kWh)
- The energy used by a 1 kW appliance running for 1 hour. It is the unit SP Group bills for, and it means kilowatt times hour, not kilowatts per hour.
Key formulas
Current
I = Q ÷ t
Q is the charge in coulombs (C), t is the time in seconds (s) and I is the current in amperes (A). Convert mA to A before substituting (1 mA = 0.001 A).
Resistance
R = V ÷ I (V = IR, I = V ÷ R)
V is in volts, I in amperes and R in ohms (Ω). For a fixed p.d., a larger resistance means a smaller current.
Series and parallel rules
Series: V(source) = V₁ + V₂ Parallel: I(source) = I₁ + I₂
In series the current is the same at every point and the source p.d. is shared. In parallel the branch currents add up to the source current and each branch gets the full source p.d.
Electrical power
P = VI
P is in watts (W), V in volts (V) and I in amperes (A). Rearrange to I = P ÷ V to find the current an appliance draws, for example when choosing a fuse.
Electrical energy
E = Pt
E is in joules if P is in W and t in seconds. E is in kWh if P is in kW and t in hours. 1 kWh = 3.6 × 10⁶ J.
Cost of electricity
Cost = energy used (kWh) × price per kWh
Find the energy in kWh first. Give cost answers to two decimal places with the dollar sign.
Worked example
An air-conditioner rated 2400 W runs for 5 hours every night for 30 days. Electricity costs $0.32 per kWh. Calculate (a) the energy used in kWh, and (b) the cost for the month.
- 1Convert the power to kilowatts: P = 2400 W = 2400 ÷ 1000 kW = 2.4 kW.
- 2Find the total time in hours: t = 5 hours per day × 30 days = 150 hours.
- 3Calculate the energy in kilowatt-hours: E = Pt = 2.4 kW × 150 h = 360 kWh.
- 4Calculate the cost: Cost = 360 × 0.32 = 115.20, so the monthly cost of running the air-conditioner is $115.20.
Watch out: Do not mix units in E = Pt. Using 2400 W with hours gives 360 000, which is wrong, so convert the power to kW and the time to hours before substituting.
Common mistakes
Thinking current gets used up
Wrong: The bulb uses up current, so an ammeter after the bulb should read less than one before it.
Right: Current is not used up. In a series circuit the current is the same at every point, and the bulb converts the energy carried by the charges, not the charges themselves.
Swapping the ammeter and voltmeter
Wrong: Connecting the voltmeter in series with a component, or the ammeter in parallel across it.
Right: The ammeter goes in series so that the current flows through it. The voltmeter goes in parallel across the component. A voltmeter in series lets almost no current flow, and an ammeter in parallel draws a dangerously large current.
Saying the fuse protects the user from shock
Wrong: The fuse protects the person using the appliance from electric shock.
Right: The fuse protects the appliance and wiring from overheating and fire. The earth wire protects the user by carrying the fault current to the ground, which blows the fuse.
Questions students ask
Why are homes in Singapore wired in parallel?
In parallel, every appliance receives the full 230 V mains p.d. and can be switched on and off independently. One faulty appliance also does not black out the house. In series, each appliance would get only a fraction of 230 V, and one blown bulb would cut the current to every socket and light.
What is the difference between a series and a parallel circuit?
A series circuit has one path, so the current is the same at every point and the source p.d. is shared among the components. In a parallel circuit the current splits at a junction and recombines. Every branch receives the full source p.d. and works independently.
How do you choose the correct fuse rating for an appliance?
Choose the smallest rating that is slightly above the normal operating current. If only the power is given, find the current with I = P ÷ V first. For example, a 1100 W kettle on 230 V mains draws I ≈ 4.8 A, so a 5 A fuse is suitable. The fuse must be fitted in the live wire.
How does the earth wire stop you getting an electric shock?
If the live wire touches a metal casing, the earth wire provides a low-resistance path from the casing to the ground. A large current flows through the earth wire rather than through the user. This current exceeds the fuse rating, so the fuse melts, breaks the circuit and disconnects the appliance.
In the full PDF
- •Labelled circuit diagrams and the cut-open cable diagram showing each insulation layer
- •The full table of all eight circuit symbols and what each component does
- •Further worked examples, including spotting wiring errors, finding R, I and V, choosing a fuse and why wet hands matter
- •The three effects of an electric current (heating, magnetic and chemical) with everyday applications
- •All eight misconceptions to un-learn, plus exam technique for Topic 13
- •A formula sheet at a glance and a summary for every section