What you'll learn
This revision guide covers all aspects of electrical circuits required for WJEC GCSE Physics examinations. You'll develop a thorough understanding of current, voltage, and resistance, learn to analyse both series and parallel circuits, and apply key equations to solve circuit problems. These concepts form the foundation for many exam questions worth significant marks.
Key terms and definitions
Current — the rate of flow of charge around a circuit, measured in amperes (A), with one ampere equal to one coulomb of charge passing a point per second.
Potential difference (voltage) — the energy transferred per unit charge between two points in a circuit, measured in volts (V).
Resistance — the opposition to current flow in a component or conductor, measured in ohms (Ω).
Electromotive force (e.m.f.) — the energy supplied by a cell or battery per unit charge passing through it, measured in volts (V).
Power — the rate of energy transfer in a circuit, measured in watts (W).
Charge — a physical property of matter that causes it to experience a force in an electromagnetic field, measured in coulombs (C).
Conventional current — the flow of charge from positive to negative terminal (opposite to electron flow).
Ohmic conductor — a component that obeys Ohm's law, where current is directly proportional to potential difference at constant temperature.
Core concepts
Electric charge and current
Electric current represents the flow of charge carriers through a conductor. In metals, these charge carriers are free electrons moving from the negative to positive terminal, though conventional current is defined as flowing from positive to negative.
The relationship between charge, current, and time is given by:
Q = I × t
Where:
- Q = charge (coulombs, C)
- I = current (amperes, A)
- t = time (seconds, s)
Current is measured using an ammeter, which must be connected in series with the component being measured. Digital ammeters have effectively zero resistance and do not affect the circuit.
Key points about current:
- Current is the same at all points in a series circuit
- Current is conserved at junctions in parallel circuits
- Metals conduct electricity because they contain delocalised electrons
- Current in circuits is typically measured in milliamperes (mA) for small currents, where 1 A = 1000 mA
Potential difference and electromotive force
Potential difference (often called voltage) represents the energy transferred by charge carriers as they move between two points. A battery's e.m.f. represents the total energy supplied per coulomb of charge.
The relationship between energy, charge, and potential difference is:
E = Q × V
Where:
- E = energy transferred (joules, J)
- Q = charge (coulombs, C)
- V = potential difference (volts, V)
Potential difference is measured using a voltmeter, which must be connected in parallel across the component being measured. Voltmeters have very high resistance to prevent current flowing through them.
Important distinctions:
- E.m.f. is the energy supplied per unit charge by the source
- P.d. is the energy transferred per unit charge across a component
- In an ideal circuit with no internal resistance, e.m.f. equals the sum of all p.d.s
- Voltmeters measure the energy difference between two points
Resistance and Ohm's law
Resistance quantifies how difficult it is for current to flow through a component. Ohm's law states that for an ohmic conductor at constant temperature:
V = I × R
Where:
- V = potential difference (volts, V)
- I = current (amperes, A)
- R = resistance (ohms, Ω)
This can be rearranged to find current (I = V ÷ R) or resistance (R = V ÷ I).
Factors affecting resistance:
- Length — resistance increases proportionally with length
- Cross-sectional area — resistance decreases as area increases
- Material — different materials have different resistivities
- Temperature — for most conductors, resistance increases with temperature
Ohmic vs non-ohmic components:
- Ohmic conductors: fixed resistors, metal wires at constant temperature (straight line through origin on I-V graph)
- Non-ohmic components: filament lamps, diodes, thermistors (curved I-V graphs)
Series circuits
In a series circuit, components are connected end-to-end in a single loop. This configuration has specific characteristics:
Current in series circuits:
- Current is identical at all points
- I₁ = I₂ = I₃ (for any number of components)
Potential difference in series circuits:
- Total p.d. equals the sum of individual p.d.s
- V_total = V₁ + V₂ + V₃
Resistance in series circuits:
- Total resistance equals the sum of individual resistances
- R_total = R₁ + R₂ + R₃
Practical applications:
- Christmas tree lights (older sets) — if one bulb fails, all go out
- Voltage dividers — used to obtain specific voltages
- Adding a series resistor limits current through sensitive components
Parallel circuits
In a parallel circuit, components are connected across common points, creating multiple pathways for current.
Current in parallel circuits:
- Total current equals the sum of currents in each branch
- I_total = I₁ + I₂ + I₃
Potential difference in parallel circuits:
- P.d. across each parallel branch is identical
- V₁ = V₂ = V₃ = V_total
Resistance in parallel circuits: For two resistors in parallel:
- 1/R_total = 1/R₁ + 1/R₂
Or: R_total = (R₁ × R₂)/(R₁ + R₂)
For multiple resistors:
- 1/R_total = 1/R₁ + 1/R₂ + 1/R₃
Important characteristics:
- Adding parallel resistors decreases total resistance
- Total resistance is always less than the smallest individual resistance
- If one component fails, others continue to function
- Household circuits use parallel connections
Power and energy in circuits
Electrical power represents the rate at which energy is transferred in a circuit. Three equivalent equations for power are:
P = I × V P = I² × R P = V² ÷ R
Where:
- P = power (watts, W)
- I = current (amperes, A)
- V = potential difference (volts, V)
- R = resistance (ohms, Ω)
The choice of equation depends on known quantities.
Energy transferred can be calculated using:
E = P × t or E = I × V × t
Where:
- E = energy (joules, J)
- t = time (seconds, s)
For household electricity calculations, energy is often measured in kilowatt-hours (kWh):
- 1 kWh = 3,600,000 J
- Energy (kWh) = Power (kW) × Time (hours)
Applications:
- Choosing appropriate fuses (based on current calculations)
- Understanding electricity costs
- Designing safe circuits with appropriate cable thickness
Circuit components and symbols
Standard circuit symbols must be learned for WJEC examinations:
Essential components:
- Cell (single line short, single line long)
- Battery (multiple cells)
- Switch (open or closed)
- Fixed resistor (rectangle)
- Variable resistor (rectangle with arrow)
- Lamp/bulb (circle with cross)
- Fuse (rectangle with line through)
- LED (circle with arrows indicating light)
- Diode (triangle and line)
- Thermistor (rectangle with temperature symbol)
- LDR (light-dependent resistor — rectangle in circle with arrows)
- Ammeter (circle with A)
- Voltmeter (circle with V)
Special components:
- Thermistor — resistance decreases as temperature increases (useful in temperature sensors)
- LDR — resistance decreases as light intensity increases (useful in automatic lighting)
- Diode — allows current in one direction only
- LED — emits light when current flows, requires series resistor to limit current
Worked examples
Example 1: Series circuit calculation
Question: A 12 V battery is connected to two resistors in series: 3 Ω and 5 Ω. Calculate: (a) the total resistance [1 mark] (b) the current in the circuit [2 marks] (c) the potential difference across the 5 Ω resistor [2 marks]
Solution:
(a) R_total = R₁ + R₂ = 3 + 5 = 8 Ω ✓
(b) Using V = I × R, rearranged to I = V ÷ R ✓ I = 12 ÷ 8 = 1.5 A ✓
(c) V = I × R ✓ V = 1.5 × 5 = 7.5 V ✓
Mark scheme notes: Part (a) requires correct addition. Part (b) needs equation stated or rearrangement shown, plus correct substitution. Part (c) requires correct use of current from part (b).
Example 2: Parallel circuit calculation
Question: Two resistors of 6 Ω and 12 Ω are connected in parallel to a 9 V supply. (a) Calculate the total resistance of the circuit. [2 marks] (b) Calculate the current drawn from the supply. [2 marks]
Solution:
(a) 1/R_total = 1/R₁ + 1/R₂ ✓ 1/R_total = 1/6 + 1/12 = 2/12 + 1/12 = 3/12 R_total = 12/3 = 4 Ω ✓
Alternative method using product/sum: R_total = (6 × 12)/(6 + 12) = 72/18 = 4 Ω
(b) I = V ÷ R ✓ I = 9 ÷ 4 = 2.25 A ✓
Mark scheme notes: For parallel resistance, either reciprocal method or product/sum method is acceptable. Must show working for full marks.
Example 3: Power and energy calculation
Question: A 3 kW electric heater is used for 2.5 hours. (a) Calculate the energy transferred in kWh. [1 mark] (b) Calculate the energy transferred in joules. [2 marks] (c) If the supply voltage is 230 V, calculate the current. [2 marks]
Solution:
(a) Energy = Power × Time = 3 × 2.5 = 7.5 kWh ✓
(b) Energy in joules = 7.5 × 3,600,000 ✓ = 27,000,000 J or 2.7 × 10⁷ J ✓
(c) P = I × V, rearranged to I = P ÷ V ✓ I = 3000 ÷ 230 = 13.04 A (accept 13 A) ✓
Mark scheme notes: Power must be in watts for part (c). Accept answers to 2-3 significant figures.
Common mistakes and how to avoid them
Confusing series and parallel rules — Remember: series circuits have same current everywhere, parallel circuits have same p.d. across each branch. Create a comparison table to memorise these differences.
Incorrect ammeter and voltmeter connections — Ammeters go IN SERIES (current must flow through them), voltmeters go IN PARALLEL (connected across components). Breaking the circuit mentally helps: ammeters break the circuit, voltmeters don't.
Forgetting to rearrange equations — V = I × R is only directly useful if you know I and R. Always identify what you're looking for first, then rearrange before substituting values. Write the rearranged equation clearly.
Unit errors — Ensure all units match the equation requirements. Convert mA to A (÷1000), kW to W (×1000), and hours to seconds (×3600) before calculating. Write conversions explicitly in exam answers.
Adding parallel resistances incorrectly — NEVER simply add resistances in parallel. Always use 1/R_total = 1/R₁ + 1/R₂ or the product/sum shortcut for two resistors. Check that parallel resistance is smaller than the smallest individual resistor.
Misinterpreting I-V graphs — The gradient of an I-V graph for ohmic conductors equals 1/R, not R itself. A steeper gradient means lower resistance because more current flows for a given voltage.
Exam technique for "Electrical Circuits"
Command word recognition — "Calculate" requires a numerical answer with working and units (usually 2-3 marks). "State" or "Give" needs a brief answer without explanation (1 mark). "Explain" requires reasoning using physics principles (2-4 marks). Always check the mark allocation to judge answer length.
Show all working — Even if your final answer is incorrect, method marks are awarded for correct equations and appropriate substitutions. Write equations in symbol form first, then substitute values, then calculate. Never just write a final number.
Unit management — Include units with every final answer unless specifically told otherwise. Common circuit units: A (amperes), V (volts), Ω (ohms), W (watts), J (joules), C (coulombs), s (seconds). Missing units typically costs one mark.
Circuit diagram questions — Use a ruler for straight lines. Ensure components are correctly drawn using standard symbols. Circuits should form complete loops. Label all values clearly (e.g., "6 V", "3 Ω"). Ammeter and voltmeter placements are frequently tested.
Quick revision summary
Electrical circuits involve current (charge flow), potential difference (energy per unit charge), and resistance (opposition to current). Series circuits have identical current throughout and resistances add directly. Parallel circuits have identical p.d. across branches and resistances combine reciprocally. Key equations: Q = I × t, V = I × R, P = I × V (and alternatives). Energy = P × t. Special components include thermistors, LDRs, and diodes. Always show working, include units, and check ammeter/voltmeter placement in diagrams.