Refer to the circuit shown. What will be the total power dissipation in the circuit if $P$ is the power dissipated in $R_1$ ? It is given that $R_2=4 R_1$ and $R_3=12 R_1$ are .......... $P$
Medium
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(a)
$\frac{E}{16 R} R_3=12 R_1$
$R_{\text {net }}=4 R_1$
$i=\frac{E}{4 R_1}$
$P=\frac{E^2 R_1}{16 R_1^2}=\frac{E^2}{16 R_1}$
$P_2=\frac{9 E^2}{256 R_1{ }^2} \cdot 4 R_1=\frac{9 P}{4}$
$P_3=\frac{E^2}{256 R_1{ }^2} \cdot 12 R_1=\frac{3 E^2}{64 R_1}=\frac{3 P}{4}$
$P+\frac{9 P}{4}+\frac{3 P}{4}=\frac{16 P}{4}=4P$
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