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

• A. $ R $
• B. $ 2R $
• C. $ \frac{R}{4} $
• D. $ \frac{R}{2} $

Answer 1

Answer: (C)

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