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

The power factor of a series LCR circuit is given by $\cos \phi = \dfrac{R}{Z}$.

Substituting the given values:

$\dfrac{8}{10} = \dfrac{100}{Z}$

$Z = \dfrac{100 \times 10}{8} = 125\ \Omega$

The impedance $Z$ of the circuit is also given by:

$Z = \sqrt{R^2 + (X_L - X_C)^2}$

Squaring both sides and substituting the values of $Z$ and $R$:

$(125)^2 = (100)^2 + (X_L - X_C)^2$

$15625 = 10000 + (X_L - X_C)^2$

$(X_L - X_C)^2 = 5625$

Taking the square root on both sides:

$X_L - X_C = \pm 75\ \Omega$

Since it is given that $X_L > X_C$, we take the positive value:

$X_L - X_C = 75\ \Omega$

Substituting $X_L = 150\ \Omega$:

$150 - X_C = 75$

$X_C = 150 - 75 = 75\ \Omega$

Answer: $75\ \Omega$