A series LCR circuit is connected to an AC source of 220   V , 50   Hz . The circuit contains a…

Power factor in LCR circuit is given by, 

$\cos \varphi =\frac{R}{Z}$, where, $Z$ is the total impedance of the circuit.

So, $\cos \varphi =\frac{R}{\sqrt{R^2+{\left(X_C-X_L\right)}^2}}$

Putting the values, we have

$\Rightarrow \cos \varphi =\frac{80}{\sqrt{(80{)}^2+(60{)}^2}}$

$\Rightarrow \cos \varphi =\frac{80}{100}\Rightarrow \frac{8}{10}$

Thus, the value of $x=8$.