A heater coil connected to a supply of a $220\, V$ is dissipating some power ${P_1}.$ The coil is cut into half and the two halves are connected in parallel. The heater now dissipates a power ${P_2}.$ The ratio of power ${P_1}\,\,:\,\,{P_2}$ is
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(c) $P = \frac{{{V^2}}}{R}$. If resistance of heater coil is $R$, then resistance of parallel combination of two halves will be $\frac{R}{4}$
So $\frac{{{P_1}}}{{{P_2}}} = \frac{{{R_2}}}{{{R_1}}} = \frac{{R/4}}{R} = \frac{1}{4}$
So $\frac{{{P_1}}}{{{P_2}}} = \frac{{{R_2}}}{{{R_1}}} = \frac{{R/4}}{R} = \frac{1}{4}$
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