Circuit reasoning: series, parallel and power

Current is the rate of charge flow. Potential difference describes energy transferred per unit charge. Resistance relates potential difference to current for an ohmic conductor under the relevant conditions: V = IR.

Worked example: a 6-ohm resistor carries 0.5 A. Its potential difference is 0.5 x 6 = 3 V. The units are important: use amperes rather than milliamperes unless you convert first. A current of 500 mA is 0.5 A.

Resistors in series add: 2 ohms and 4 ohms give 6 ohms. The same current flows through each component in a simple series path. The potential differences across the components add to the total supplied.

For two equal resistors in parallel, the equivalent resistance is half the resistance of one resistor. Two 8-ohm resistors therefore give 4 ohms. Parallel branches share the same potential difference, while the total current is the sum of the branch currents. Do not use the series addition rule for a parallel arrangement.

Electrical power is P = VI. A device operating at 12 V with a current of 2 A uses 24 W. Energy transferred over a time t is E = Pt when power is constant; over 10 s this gives 240 J.

Practice:
1. Find voltage for 3 A through 5 ohms.
2. Find total resistance for 3 and 7 ohms in series.
3. Find equivalent resistance for two 6-ohm resistors in parallel.
4. Find power for a device using 9 V and 0.4 A.

Answers: 1 15 V; 2 10 ohms; 3 3 ohms; 4 3.6 W.

These are paper-based calculations. Do not test ideas by opening appliances or connecting anything to mains electricity. Draw the circuit, label quantities and explain the current paths before calculating. A correct numerical answer should also fit the arrangement you drew.