Question

In the circuit, given power factor of box is 0.5 and power factor of circuit is $\frac{\sqrt{3}}{2}$. Current is leading the voltage. Resistance used in box is.

Answer 1

Power factor is $\cos \varphi \Rightarrow$ for box $\cos \varphi =0.5i.e\varphi ={60}^{\circ }$
$\Rightarrow tan{60}^{\circ }=\frac{X_C}{R}$ .....(1)

For full circuit:
$\Rightarrow cos\varphi =\frac{\sqrt{3}}{2}\Rightarrow \varphi ={30}^{\circ }$
$tan{30}^{\circ }=\frac{X_C}{R+10}$ .....(2)

By (1) & (2)
$3=\frac{R+10}{R}$

$R=5\Omega$