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(B) The current $i$ flows through $R_1 = R$. The power dissipated in $R_1$ is $P = i^2 R$.In the parallel combination of $R_2 = R$ and $R_3 = 2R$,the

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$\frac{4 P}{9}$

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(B) The current $i$ flows through $R_1 = R$. The power dissipated in $R_1$ is $P = i^2 R$.In the parallel combination of $R_2 = R$ and $R_3 = 2R$,the current $i$ divides. Let $i_2$ be the current through $R_2$ and $i_3$ be the current through $R_3$.By the current divider rule,$i_2 = i 	imes \frac{R_3}{R_2 + R_3} = i 	imes \frac{2R}{R + 2R} = i 	imes \frac{2R}{3R} = \frac{2}{3}i$.The thermal power dissipated in $R_2$ is $P_2 = i_2^2 R_2 = (\frac{2}{3}i)^2 R = \frac{4}{9} i^2 R$.Since $P = i^2 R$,we have $P_2 = \frac{4}{9} P$.

In the circuit shown,the thermal power dissipated in $R_1$ is $P$. The thermal power dissipated in $R_2$ is

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