Question

A circuit operating at $\frac{360}{2\pi }Hz$ contains a $1\mu F$ capacitor and a $20\Omega$ resistor. How large an inductor must be added in series to make the phase angle for the circuit zero? Calculate the current (in A) in the circuit if the applied voltage is $120V$.

Write value of $\frac{L}{1.1}+I$.

Answer 1

Given : $f=\frac{360}{2\pi }$ Hz, $C={10}^{-6}F$ and $R=20\Omega$

For phase angle $\varphi =0$, we must get $X_L=X_C$
Or $2\pi fL=\frac{1}{2\pi fC}$
Thus inductance $L=\frac{1}{(2\pi f{)}^2}C$
$\therefore$ $L=\frac{1}{(360{)}^2\times {10}^{-6}}$ $=7.7H$
Since $X_L=X_C$, we get impedance of the circuit $Z=R=20\Omega$

Thus current in the circuit $I=\frac{V}{Z}=\frac{V}{R}$
$⟹I=\frac{120}{20}=6A$