Edexcel A-Level Physics AS 2.4.68 Combining Resistances in Series and Parallel Questions

Practise Edexcel A-Level Physics combined resistance in series and parallel using derivations, equivalent circuits and resistor networks.

Exam points

derive total resistance for series circuits from VT = V1 + V2 and V = IR
calculate unknown resistance in mixed series-parallel networks from current and voltage
recognise short circuits and equivalent-resistance expressions in resistor networks

[Maximum number: 3]

Drivers use car headlights to emit light in dark conditions.
The graph shows how current I varies with potential difference V for a car headlight.

Figure for Question Edexcel A-Level Physics AS 2.4.68 Combining Resistances in Series and Parallel Questions question 1 — Edexcel A-Level Physics AS

The headlight will emit light when it dissipates at least 35 W of power.

In a car, two headlights are connected in parallel with a 12.0 V battery. The battery has negligible internal resistance.

A student writes the following statement.

When connected to the 12.0 V battery, the combined resistance of two headlights in parallel is one quarter of the combined resistance of two headlights in series.

Deduce whether the student is correct.
Your answer should include calculations using data from the graph.

From the graph, one headlight at $12.0\,\mathrm{V}$ takes $4.6\,\mathrm{A}$ , so $R=V/I=2.61\,\Omega$ and two in parallel have $R_T=1.30\,\Omega$ . At $6.0\,\mathrm{V}$ , one takes about $3.2\,\mathrm{A}$ , so two in series have $R_T=2(6.0/3.2)=3.76\,\Omega$ . The ratio is 3.76/1.30=2.9, not 4, so the student is incorrect.

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Edexcel A-Level Physics AS 2.4.68 Combining Resistances in Series and Parallel Questions question 1