What you'll learn
Current Electricity forms a substantial component of CIE IGCSE Physics, typically accounting for 15-20% of exam questions. This topic examines how electrical charge flows through circuits, the relationships between current, voltage and resistance, and how to analyse series and parallel circuits. Questions range from straightforward calculations to multi-step circuit analysis and practical applications.
Key terms and definitions
Electric current — the rate of flow of electric charge, measured in amperes (A). One ampere equals 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). One volt equals one joule per coulomb.
Resistance — the opposition to current flow in a component, measured in ohms (Ω). A component has a resistance of one ohm if a potential difference of one volt causes a current of one ampere.
Electromotive force (e.m.f.) — the energy supplied by a cell or power supply per unit charge, measured in volts (V). Unlike potential difference, e.m.f. refers specifically to energy supplied rather than energy transferred.
Conventional current — the flow of positive charge from the positive terminal to the negative terminal of a power supply, opposite to the actual electron flow direction.
Electrical power — the rate of energy transfer in a circuit, measured in watts (W). One watt equals one joule per second.
Core concepts
Electric charge and current
Electric current results from the movement of charge carriers through a conductor. In metallic conductors, these carriers are free electrons that drift through the metal lattice when a potential difference is applied.
The relationship between charge, current and time:
Q = I × t
Where:
- Q = charge in coulombs (C)
- I = current in amperes (A)
- t = time in seconds (s)
Current is measured using an ammeter, which must be connected in series with the component being measured. The ammeter should have negligible resistance to avoid affecting the circuit behaviour. Conventional current direction flows from positive to negative, though electrons actually move from negative to positive.
Potential difference and electromotive force
Potential difference across a component represents the energy transferred when charge passes through it. A lamp converts electrical energy to light and heat; a motor converts electrical energy to kinetic energy.
Potential difference is measured using a voltmeter, which must be connected in parallel across the component. A voltmeter should have very high resistance to draw minimal current from the circuit.
The relationship between energy, charge and voltage:
E = Q × V
Where:
- E = energy in joules (J)
- Q = charge in coulombs (C)
- V = potential difference in volts (V)
Electromotive force measures the energy supplied per unit charge by a cell or generator. In real cells, the terminal potential difference is less than the e.m.f. when current flows due to internal resistance.
Resistance and Ohm's law
Ohm's law states that for a conductor at constant temperature, the current through it is directly proportional to the potential difference across it:
V = I × R
Where:
- V = potential difference in volts (V)
- I = current in amperes (A)
- R = resistance in ohms (Ω)
Components that obey Ohm's law are called ohmic conductors. When potential difference is plotted against current for an ohmic conductor, the graph is a straight line through the origin with gradient equal to resistance.
Non-ohmic components do not show this linear relationship:
- Filament lamp: As current increases, temperature rises, increasing resistance. The I-V graph curves with decreasing gradient.
- Thermistor: Resistance decreases as temperature increases. Used in temperature sensors and fire alarms.
- Light-dependent resistor (LDR): Resistance decreases as light intensity increases. Used in automatic lighting systems and light meters.
- Diode: Allows current in one direction only (forward bias) with very high resistance in reverse bias. The I-V graph shows near-zero current until a threshold voltage.
Series and parallel circuits
Series circuits have components connected end-to-end in a single loop:
- Current is the same at all points: I₁ = I₂ = I₃
- Total potential difference equals the sum of individual potential differences: V_total = V₁ + V₂ + V₃
- Total resistance equals the sum of individual resistances: R_total = R₁ + R₂ + R₃
Adding more components in series increases total resistance and decreases current.
Parallel circuits have components connected across common points with multiple current paths:
- Potential difference is the same across each branch: V₁ = V₂ = V₃
- Total current equals the sum of branch currents: I_total = I₁ + I₂ + I₃
- For resistance: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃
Adding more components in parallel decreases total resistance and increases total current drawn from the supply.
For two resistors in parallel, the combined resistance can be calculated:
R_total = (R₁ × R₂)/(R₁ + R₂)
Electrical power and energy
Electrical power is the rate of energy transfer in a circuit. Three equivalent equations relate power to current, voltage and resistance:
P = V × I
P = I² × R
P = V²/R
Where:
- P = power in watts (W)
- V = potential difference in volts (V)
- I = current in amperes (A)
- R = resistance in ohms (Ω)
The choice of equation depends on which quantities are known. For resistors with known resistance and current, P = I² × R is most convenient. For components with known voltage and current, P = V × I is simplest.
Electrical energy transferred over time:
E = P × t or E = V × I × t
Where:
- E = energy in joules (J)
- t = time in seconds (s)
For practical energy billing, energy is measured in kilowatt-hours (kW h), where 1 kW h = 3,600,000 J.
Mains electricity and safety
Mains electricity in most countries is supplied as alternating current (a.c.) at 230 V, 50 Hz. Household circuits include several safety features:
Fuses are thin wires that melt and break the circuit if current exceeds the rated value, protecting against overheating. The fuse rating should be slightly higher than the normal operating current of the appliance.
Circuit breakers perform the same function as fuses but can be reset rather than replaced. They contain an electromagnetic switch or thermal switch that trips when excess current flows.
Earth wire provides a low-resistance path to ground for fault currents. If a live wire touches a metal case, high current flows through the earth wire, causing the fuse to blow or circuit breaker to trip.
The three-pin plug contains:
- Live wire (brown): alternates between positive and negative, supplies current
- Neutral wire (blue): completes the circuit, close to 0 V
- Earth wire (green and yellow stripes): safety connection to ground
Double-insulated appliances with plastic cases do not require an earth connection.
Worked examples
Example 1: Calculating charge flow
Question: A current of 3.5 A flows through a lamp for 2 minutes. Calculate the charge that passes through the lamp. [2 marks]
Solution:
Step 1: Convert time to seconds t = 2 × 60 = 120 s [1 mark]
Step 2: Use Q = I × t Q = 3.5 × 120 Q = 420 C [1 mark]
Example 2: Series circuit calculation
Question: A 12 V battery is connected to two resistors in series: 4 Ω and 8 Ω. (a) Calculate the total resistance. [1 mark] (b) Calculate the current in the circuit. [2 marks] (c) Calculate the potential difference across the 8 Ω resistor. [2 marks]
Solution:
(a) R_total = R₁ + R₂ = 4 + 8 = 12 Ω [1 mark]
(b) Using V = I × R, rearranged: I = V/R I = 12/12 I = 1.0 A [2 marks: 1 for rearrangement, 1 for answer]
(c) Using V = I × R for the 8 Ω resistor V = 1.0 × 8 V = 8.0 V [2 marks: 1 for method, 1 for answer]
Example 3: Power calculation
Question: A 230 V electric heater draws a current of 8.7 A. (a) Calculate the power of the heater. [2 marks] (b) Calculate the energy transferred if the heater operates for 30 minutes. Give your answer in kW h. [3 marks]
Solution:
(a) P = V × I P = 230 × 8.7 P = 2001 W (or 2.0 kW) [2 marks]
(b) Time = 30 minutes = 0.5 hours E = P × t E = 2.0 × 0.5 E = 1.0 kW h [3 marks: 1 for time conversion, 1 for method, 1 for answer]
Common mistakes and how to avoid them
Confusing current and charge: Current is the rate of flow of charge, not the amount of charge. Use Q = I × t to relate them, and remember current is measured in amperes while charge is measured in coulombs.
Ammeter and voltmeter connections: A common error is connecting the ammeter in parallel or the voltmeter in series. Remember: ammeters measure current flowing through (series connection), voltmeters measure potential difference across (parallel connection).
Adding parallel resistances incorrectly: Students often add parallel resistances like series resistances. The total resistance in parallel is always less than the smallest individual resistance. Use 1/R_total = 1/R₁ + 1/R₂ + 1/R₃, not R_total = R₁ + R₂ + R₃.
Wrong power equation: Selecting P = V²/R when current and resistance are given, or P = I²R when voltage and resistance are given. Choose the equation that matches the available information: P = VI when both are known, P = I²R when current is known, P = V²/R when voltage is known.
Unit confusion in energy calculations: Mixing joules and kilowatt-hours or forgetting to convert time to appropriate units. For E = Pt in joules, time must be in seconds; for energy in kW h, power must be in kW and time in hours.
Misunderstanding e.m.f. vs terminal p.d.: Treating e.m.f. and terminal potential difference as identical. E.m.f. is the energy supplied per unit charge by the source; terminal p.d. is what appears across the external circuit and is less than e.m.f. when current flows due to internal resistance.
Exam technique for Current Electricity
Calculation questions typically award 1 mark for substituting correct values into the correct equation, and 1 mark for the correct answer with units. Always show your working clearly and include units in final answers.
Circuit diagram questions require you to correctly add ammeters in series and voltmeters in parallel. Use standard circuit symbols and ensure all connections are clear with straight lines. CIE examiners deduct marks for ambiguous junctions or non-standard symbols.
Explain/describe questions on resistance in series vs parallel circuits need comparative statements. Don't just state facts about one configuration—explicitly compare both, e.g., "In series, current is the same everywhere, whereas in parallel, current splits between branches."
Practical questions may ask you to describe how to investigate the relationship between current and voltage. Include detail on variable resistor use, repeated measurements, control variables (temperature for Ohm's law), and safety considerations (appropriate voltage/current levels).
Quick revision summary
Current (I) is the rate of flow of charge (Q = It). Potential difference (V) is energy per unit charge. Resistance (R) opposes current flow; Ohm's law states V = IR for ohmic conductors. In series: same current, voltages add, resistances add. In parallel: same voltage, currents add, 1/R_total = 1/R₁ + 1/R₂. Power equations: P = VI = I²R = V²/R. Energy E = Pt = VIt. Ammeters connect in series, voltmeters in parallel. Safety devices include fuses, circuit breakers and earth wires.