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In India electricity is supplied for domestic use at 220 V. It is supplied at 110 V in USA. If the resistance of a 60W bulb for use in India is R, The resistance of a 60W bulb for use in USA will be :-
A
2R
B
$\dfrac{R}{4}$
C
$\dfrac{R}{2}$
D
R
Detailed Solution
Use power $P = \dfrac{V^2}{R}$, so $R = \dfrac{V^2}{P}$.
For India: $R = \dfrac{220^2}{60}$
For USA: $R' = \dfrac{110^2}{60}$
$\dfrac{R'}{R} = \dfrac{110^2}{220^2} = \left(\dfrac{1}{2}\right)^2 = \dfrac{1}{4}$
$\Rightarrow R' = \dfrac{R}{4}$
So the 60 W bulb meant for the USA has resistance $\dfrac{R}{4}$.
For India: $R = \dfrac{220^2}{60}$
For USA: $R' = \dfrac{110^2}{60}$
$\dfrac{R'}{R} = \dfrac{110^2}{220^2} = \left(\dfrac{1}{2}\right)^2 = \dfrac{1}{4}$
$\Rightarrow R' = \dfrac{R}{4}$
So the 60 W bulb meant for the USA has resistance $\dfrac{R}{4}$.