A circuit operating at $\dfrac{360}{2\pi }$ Hz $\Omega$ contains a 1 F $\mu$ capacitor and a 20 resistor. The inductor must be added in series to make the phase angle for the circuit zero is

To make phase angle zero, circuit should be purely resistive, so, reactance should be zero.

Hence, $X_L = X_C$

$wL = \dfrac{1}{\omega C}$

$L = \dfrac{1}{\omega^2 C}$

$L= \dfrac{1}{(2\pi f)^2C}$

$L= \dfrac{1}{(2\pi \dfrac{360}{2\pi})^2\times 10^{-6}}$

$L= \dfrac{10^6}{129600}$

$L= 7.7H$