Series or parallel?

Electricity and Magnetism Level 1

Jane hosted a party in her house but, unfortunately, the fuse has blown. She has an ideal battery (with zero resistance) and two bulbs. To produce a greater brightness (greater total power by the bulbs), should she connect the bulbs in series or in parallel with the battery?

Note:

The equivalent resistance $(R_{\text{net}})$ of two resistors $R_1$ and $R_2$ in series is $R_1+R_2,$ and in parallel $\frac{R_1R_2}{R_1+R_2}$ .
The power produced in a circuit is $\frac{V^2}{R_{\text{net}}}$ or $i^2 R_{\text{net}}$ .

Parallel with the battery Series with the battery They are both the same

1 solution

Tom Engelsman
Feb 17, 2017

For the series circuit: the current equals $I = \frac{V}{2R}$ , and the total power computes to $P_s = I^{2}(2R) = \left(\frac{V}{2R}\right)^{2}(2R) = \frac{V^{2}}{2R}.$

For the parallel circuit, each bulb measures the same voltage across them as the battery's value. Hence the total power here is $P_p = 2(\frac{V^2}{R}) = \frac{2V^{2}}{R}.$

Ultimately, $P_p = 4P_s$ , so the parallel arrangement is brighter.

We may also state the same in another way.

The power produced equals $P = \dfrac{V^2}{R_{\text{net}}}$ .

Therefore, the smaller the net resistance, the greater the power produced.

The resistance in the parallel circuit is always lesser than the series combination, therefore, the total power produced in the parallel circuit is higher.

Rohit Gupta - 4 years, 3 months ago

Series or parallel?

1 solution

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