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(C) Let the power dissipated in each resistor be $P$. Since $R_2$ and $R_3$ are in parallel,the voltage across them is the same. For equal power dissi

Vedclass · Accepted Answer

$R_2 = R_3$ and $R_1 = \frac{R_2}{4}$

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(C) Let the power dissipated in each resistor be $P$. Since $R_2$ and $R_3$ are in parallel,the voltage across them is the same. For equal power dissipation,$P = \frac{V_2^2}{R_2} = \frac{V_3^2}{R_3}$. Since $V_2 = V_3$,we must have $R_2 = R_3$. Let $R_2 = R_3 = R$. The equivalent resistance of the parallel combination is $R_p = \frac{R 	imes R}{R + R} = \frac{R}{2}$. The current through $R_1$ is $I$,and the current through each of $R_2$ and $R_3$ is $I/2$. Power dissipated in $R_1$ is $P_1 = I^2 R_1$. Power dissipated in $R_2$ is $P_2 = (I/2)^2 R_2 = \frac{I^2 R_2}{4}$. Since $P_1 = P_2$,we have $I^2 R_1 = \frac{I^2 R_2}{4}$,which gives $R_1 = \frac{R_2}{4}$. Thus,the condition is $R_2 = R_3$ and $R_1 = \frac{R_2}{4}$.

For ensuring the dissipation of the same energy in all three resistors $(R_1, R_2, R_3)$ connected as shown in the figure,their values must be related as:

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