First slide

Electrical power

Question

n identical light bulbs, each designed to draw P power from a certain supply, are joined in series across that supply. The total power which they will draw is

Easy

A

$\frac{P}{n}$
B

np
C

$\frac{P}{n^{2}}$
D

P

Solution

Let R be the resistance of each bulb. Resistance of n bulbs = n R
Current in each bulb $= i = \frac{V}{nR}$
Power drawn by each bulb
$\begin{aligned} P^{2} = i^{2} R = \frac{V^{2}}{n^{2} R^{2}} \times R \\ = \frac{V^{2}}{n^{2} R} = \frac{P}{n^{2}} (∵ R = \frac{V^{2}}{P}) \end{aligned}$
Total power drawn $= n \times (\frac{P}{n^{2}}) = \frac{P}{n}$

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