Physics

Problem

Two identical

3\,\Omega

lightbulbs are connected to a

9\,\text{V}

ideal battery. In Circuit 1 the bulbs are connected in series; in Circuit 2 the same two bulbs are connected in parallel. What is the ratio

\frac{P_{\text{parallel}}}{P_{\text{series}}}

of the power dissipated by a single bulb in the parallel circuit to that of a single bulb in the series circuit? a)

\dfrac{1}{4}

1

4

2

Intuitive explanation

The key is recognizing that total resistance changes dramatically between series and parallel, which changes the current flowing through each bulb and thus the power it dissipates. In series, resistances add, so total resistance is large and current is small; in parallel, resistances combine as reciprocals, giving small total resistance and large current. Since power depends on $I^2R$ (or $V^2/R$ ), a single bulb experiences very different conditions in each configuration.

Intuitive explanation

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