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Question

(A) Let the resistance of each heater filament be $R$ and the applied voltage be $V$. The heat produced in time $t$ is given by $H = \frac{V^2}{R_{eq}

Vedclass · Accepted Answer

$4: 1$

Vedclass · Answer

(A) Let the resistance of each heater filament be $R$ and the applied voltage be $V$. The heat produced in time $t$ is given by $H = \frac{V^2}{R_{eq}} t$.For parallel combination,the equivalent resistance is $R_p = \frac{R 	imes R}{R + R} = \frac{R}{2}$.Thus,the heat produced is $H_p = \frac{V^2}{R_p} t = \frac{V^2}{R/2} t = \frac{2V^2 t}{R}$.For series combination,the equivalent resistance is $R_s = R + R = 2R$.Thus,the heat produced is $H_s = \frac{V^2}{R_s} t = \frac{V^2}{2R} t$.The ratio of heat produced in parallel to series is $\frac{H_p}{H_s} = \frac{2V^2 t / R}{V^2 t / 2R} = 2 	imes 2 = 4$.Therefore,the ratio is $4:1$.

Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage,the ratio of heat produced in the same time for parallel to series will be:

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