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

Solution :
Since, power rating of bulb in both the countries India and USA is same, so
$$\eqalign{ & \frac{{V_1^2}}{{{R_1}}} = \frac{{V_2^2}}{{{R_2}}}\,\,\left[ {P = \frac{{{V^2}}}{R}} \right] \cr & \Rightarrow \frac{{220 \times 220}}{{{R_1}}} = \frac{{110 \times 110}}{{{R_2}}} \cr & \Rightarrow \frac{{{R_2}}}{{{R_1}}} = \frac{{110 \times 110}}{{220 \times 220}} \cr & \Rightarrow {R_2} = \frac{R}{4}\,\,\left( {\because {R_1} = R} \right) \cr} $$