Learning objectives
- Use Ohm's law in numerical problems.
- Compare series and parallel connections.
- Calculate electrical power and energy.
- Explain common household circuit choices.
Current, voltage and resistance
Electric current is the rate of flow of charge. Its SI unit is the ampere. Potential difference is the work done per unit charge and is measured in volts.
Resistance opposes current. For many conductors at constant temperature, Ohm's law states that potential difference is proportional to current: V = IR.
Series and parallel circuits
In series, the same current flows through each component and the total resistance is the sum of individual resistances. If one component breaks, the whole path is interrupted.
In parallel, each branch has the same potential difference. Household appliances are connected in parallel so they can operate independently and receive the rated voltage.
Power and energy
Electrical power is the rate at which electrical energy is converted. P = VI, and equivalent forms include P = I²R and P = V²/R.
Electrical energy equals power multiplied by time. The commercial unit is the kilowatt-hour. One kilowatt-hour is the energy used by a 1 kW device operating for one hour.
Series versus parallel: trace the paths
In a series path, the same current passes through each component. In parallel branches, each branch is connected across the supply, so each branch has the same potential difference in the idealized model.
Fault-finding thought experiment
Two lamps are connected in series. One lamp fails open-circuit. What happens to the other lamp? Now imagine the lamps are connected on separate parallel branches. Explain why the outcomes differ by tracing whether a complete conducting path remains.
Worked example: one resistor and two resistors
For a conductor behaving approximately ohmically at a constant temperature, Ohm's law relates potential difference, current and resistance: V = I × R. With 12 V across a 6 Ω resistor, current is 12 ÷ 6 = 2 A.
Now connect two 6 Ω resistors in series to the same 12 V supply. Their total resistance is 6 + 6 = 12 Ω, so the current through both is 12 ÷ 12 = 1 A. If the two 6 Ω resistors are instead connected in parallel across the supply, each branch has 12 V across it and carries 2 A. The total current from the supply is therefore 4 A, and the equivalent resistance is 3 Ω.
| Connection | Equivalent resistance | Total current |
|---|---|---|
| Series | 12 Ω | 1 A |
| Parallel | 3 Ω | 4 A |
In a series circuit, current is the same through each component. In a parallel circuit, potential difference is the same across each branch. These are idealized calculations: real supplies, wiring and components may introduce additional effects.
Power and energy example
A 60 W device operating for 2 hours uses 60 × 2 = 120 Wh, which equals 0.12 kWh. The kilowatt-hour is a unit of energy, not power. Never experiment on mains electrical wiring or appliances as part of a school exercise.
Calculate it yourself
What current flows through a 4 Ω resistor across an 8 V supply?
I = V ÷ R = 8 ÷ 4 = 2 A.
A 100 W lamp runs for 3 hours. How much energy is used in kWh?
100 W = 0.1 kW; energy = 0.1 × 3 = 0.3 kWh.
Teacher prompt: diagnose the circuit model
Ask a learner to predict what changes when a second identical lamp is added in series, then ask the same question for parallel branches. Listen for the common error that “more components always means more current everywhere.” Follow up by asking which quantity is shared in each arrangement.
Extension: annotate the circuit diagram with one statement about current and one about potential difference. This makes invisible quantities explicit without requiring a mains experiment.
One-minute circuit check
Current is charge flow per time. Potential difference is energy transferred per charge. Resistance describes opposition to current. For calculations, write known values, select V = IR, check units, and ask whether the answer is sensible.
Practice questions with explanations
Try each question before opening the answer. The explanation shows the reasoning, not only the final response.
Q1. What is electric current?
Answer: The rate of flow of electric charge.
Explanation: Current equals charge divided by time.
Q2. What is the SI unit of resistance?
Answer: The ohm (Ω).
Explanation: One ohm allows one ampere when one volt is applied.
Q3. State Ohm's law.
Answer: At constant temperature, V = IR.
Explanation: Potential difference is proportional to current for an ohmic conductor.
Q4. Find current when V = 12 V and R = 4 Ω.
Answer: 3 A.
Explanation: I = V/R = 12/4.
Q5. Find resistance when V = 9 V and I = 0.5 A.
Answer: 18 Ω.
Explanation: R = V/I = 9/0.5.
Q6. What is the equivalent resistance of 2 Ω and 3 Ω in series?
Answer: 5 Ω.
Explanation: Series resistances add directly.
Q7. Why are household appliances connected in parallel?
Answer: They receive the same voltage and operate independently.
Explanation: Switching off one branch does not open the others.
Q8. Calculate power for a 230 V appliance drawing 2 A.
Answer: 460 W.
Explanation: P = VI = 230 × 2.
Q9. How much energy does a 1.5 kW heater use in 2 hours?
Answer: 3 kWh.
Explanation: Energy = power × time = 1.5 × 2.
Q10. Why does a fuse wire melt during excessive current?
Answer: Heating increases as current rises.
Explanation: The thin fuse wire melts and opens the circuit before damage occurs.