First slide

Electrical power

Question

In India electricity is supplied for domestic use at 220 V. It is supplied at 110 V in USA. If the resistance of a 60 W bulb for use in India is R, the resistance of a 60 W bulb for use in USA will be

Easy

A

R
B

2R
C

$\frac{R}{4}$
D

$\frac{R}{2}$

Solution

Since, power rating of bulb in both the countries India and USA should be the same, so
$\begin{array}{l} ∴ \frac{V_{1}^{2}}{R_{1}} = \frac{V_{2}^{2}}{R_{2}} \\ \Rightarrow \frac{220 \times 220}{R_{1}} = \frac{110 \times 110}{R_{2}} \\ \Rightarrow \frac{R_{2}}{R_{1}} = \frac{110}{220} \times \frac{110}{220} \end{array}$
$\Rightarrow R_{2} = \frac{R}{4} (∵ R_{1} = R)$

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