Question

A series RLC circuit consists of a 20 Ω resistor, a 51 μF capacitor, and a 25 mH inductor. If
the source frequency is 50 Hz, and the circuit current is 350 mA, what is the applied voltage?
Also find the following:
(a) If the applied voltage to the circuit of above mentioned ckt is 12 V, what is the voltage
across the capacitor?
(b) In the circuit of above mentioned Ckt, what is the phase angle between the voltage
and the current?

Answer 1

The impedance is

$$Z=\sqrt{R^2+\bigg(\omega L-\frac{1}{\omega C}\bigg)^2}.$$

The voltage is

$$V=ZI=20.3\text{ V}.$$

(a) The voltage across the capacitor is

$$V_C=IX_C=\frac{I}{\omega C}=2.18\text{ V}.$$

(b) The phase angle is

$$\phi=\text{atan}\bigg[\frac{X_L-X_C}{R}\bigg]=\text{atan}\bigg[\frac{\omega L-1/(\omega C)}{R}\bigg],\\\space\\ \phi=-69.9°.$$