Physics - EMI/AC Question with Solution | TestHub

Given:

Resistance $R=30\Omega$

Capacitive reactance $X_C=20\Omega$

Inductive reactance $X_L=60\Omega$

Voltage $V=100\mathrm{V}$

The impedance of the series RLC circuit is:

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

$$Z=\sqrt{(30\Omega {)}^2+(60\Omega -20\Omega {)}^2}$$

$$Z=\sqrt{900{\Omega }^2+(40\Omega {)}^2}$$

$$Z=\sqrt{900{\Omega }^2+1600{\Omega }^2}$$

$$Z=\sqrt{2500{\Omega }^2}=50\Omega$$

The current flowing in the circuit is:

$$I=\frac{V}{Z}=\frac{100\mathrm{V}}{50\Omega }=2.0\mathrm{A}$$

The power factor of the circuit is:

$$\cos \varphi =\frac{R}{Z}=\frac{30\Omega }{50\Omega }=\frac{3}{5}$$

Therefore, a current of $2.0\mathrm{A}$ flows, and the power factor is $3/5$.