First slide

Electrical power

Question

An electric bulb, marked 40 W and 200 V is used in a circuit of supply voltage 100 V. Now its power is

Easy

A

100 W
B

40 W
C

20 W
D

10 W

Solution

Power of bulb is given by, $P = \frac{V^{2}}{R}$
$\begin{array}{l} \Rightarrow \frac{P_{2}}{P_{1}} = \frac{V_{2}^{2}}{V_{1}^{2}} (∵ R is constant) \\ \Rightarrow \frac{P_{2}}{P_{1}} = {(\frac{100}{200})}^{2} = \frac{1}{4} \Rightarrow P_{2} = \frac{P_{1}}{4} = \frac{40}{4} = 10 W \end{array}$

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