In the net work shown if $X_C=\frac{R}{\sqrt{2}}and{X}_L=R,$ ratio of power consumed in the upper branch to that in the lower branch is

 

 

(3)

$P_C=$Power consumed in the upper branch

$=\frac{V_m^{2}R}{2\left(R^2+X_C^2\right)}=\frac{V_m^{2}R}{2\left(R^2+{\displaystyle \frac{R^2}{2}}\right)}=\frac{V_m^2}{3R}$

$P_L=$ Power consumed in the lower branch

$\begin{array}{l}=\frac{V_m^{2}R}{2\left(R^2+X_L^2\right)}=\frac{V_m^{2}R}{2\left(R^2+R^2\right)}=\frac{V_m^2}{4R}\\ \therefore \frac{P_C}{P_L}=\frac{4}{3}\end{array}$