In a series circuit the resistor

PHYSICS · Multi-part · ISC · Physics · Electromagnetic Induction and Alternating Currents · Electromagnetic Induction and Alternating Currents

Problem

In a series

RLC

circuit the resistor, inductor and capacitor have the values

R = 30\,\Omega

L = 0.30\,\text{H}

and

C = 8.0\,\mu\text{F}

respectively. The r.m.s. value of the applied sinusoidal voltage is

120\,\text{V}

. (a) Show that the condition for the circuit current to lead the applied voltage by

45^{\circ}

|X_L - X_C| = R

. (b) Using the component values given, write down the quadratic equation in angular frequency

\omega

that satisfies the condition obtained in part (a). (c) Solve the quadratic equation to obtain the two possible angular frequencies. Identify which of the two lies above the resonant frequency of the circuit. (d) For the higher of the two frequencies, calculate the r.m.s. current in the circuit.

Related theory

Resonance in AC Circuits
AC Circuit Analysis
AC Fundamentals
AC applied to a series LCR circuit
Alternating Current
Series LCR circuit

Browse the problem library