Electric power

Curricula: KS3, GCSE, cycle 4, 1re (effet Joule), Sek I, AP2

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Aim

Determine the power of the lamps, \(P = U \cdot I\), and compare their brightness when they are connected in parallel and in series.

The bench

Two circuits powered by 6 V sources, with 6 V / 3 W and 6 V / 1 W lamps. At the top the lamps are connected in parallel, each with its own ammeter, and the voltmeter shows the voltage across the lamps. At the bottom they are connected in series, with an ammeter and a voltmeter on the 1 W lamp.

Procedure

1. Compare the brightness of the lamps in each circuit.
2. In the top circuit, calculate the power of each lamp: \(P = U \cdot I\), where \(U\) is the voltmeter reading.
3. In the bottom circuit, calculate the power of the 1 W lamp and estimate the voltage across the 3 W lamp: 6 V minus the voltmeter reading.

Expected result

In parallel: about 5.6 V across the lamps — part of the 6 V is lost inside the source; 3 W lamp — about 478 mA, 2.7 W; 1 W lamp — about 160 mA, 0.9 W; both fall slightly short of their rating, and the more powerful lamp is brighter. In series: the current is about 151 mA, and the 1 W lamp has about 5.09 V across it (0.77 W); across the 3 W lamp the estimate is about 0.9 V (in fact about 0.8 V — a little more is lost in the source and the ammeter), and it barely glows. The lamp with the greater resistance glows brighter.

Questions

1. Why does the low-power lamp glow brighter when the lamps are in series?
2. How much energy does the 3 W lamp consume in an hour?

Answers

1. In series both lamps carry the same current, so by \(P = I^2 R\) the lamp with the greater resistance takes more power. From the ratings, \(R = U^2 / P\) gives 36 Ω for the 1 W lamp and 12 Ω for the 3 W lamp, so the 1 W lamp takes most of the voltage: about 5.09 V and 0.77 W, against about 0.8 V and 0.12 W for the 3 W lamp.
2. \(E = P \cdot t\) = 3 W × 3600 s = 10 800 J, or 3 W·h. On this bench, in parallel, it takes about 2.7 W, which gives about 9.7 kJ in an hour.