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In India electricity is supplied for domestic use at $220 \mathrm{~V}$. It is supplied at $110 \mathrm{~V}$ in USA. If the resistance of a $60 \mathrm{~W}$ bulb for use in India is $R$, the resistance of a $60 \mathrm{~W}$ bulb for use in USA will be:
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Verified Answer
The correct answer is:
$\frac{R}{4}$
In India, $P_1=\frac{(220)^2}{R}$
In USA $\quad P_V=\frac{(110)^2}{R_0}$
As $\quad P_1=P_V$
$$
\begin{aligned}
& \Rightarrow \quad \frac{(220)^2}{R}=\frac{(110)^2}{R_V} \\
& \therefore R_V=\frac{110 \times 110}{220 \times 220} \Rightarrow f v=\frac{R}{4}
\end{aligned}
$$
In USA $\quad P_V=\frac{(110)^2}{R_0}$
As $\quad P_1=P_V$
$$
\begin{aligned}
& \Rightarrow \quad \frac{(220)^2}{R}=\frac{(110)^2}{R_V} \\
& \therefore R_V=\frac{110 \times 110}{220 \times 220} \Rightarrow f v=\frac{R}{4}
\end{aligned}
$$
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