# PHYS 2212 Module 11.5

## Resonance in an AC Circuit

11.5 Resonance in an AC Circuit

### Learning Objectives

By the end of this section, you will be able to:

• Determine the peak ac resonant angular frequency for a RLC circuit
• Explain the width of the average power versus angular frequency curve and its significance using terms like bandwidth and quality factor

### Resonance

Practice!

If the capacitive reactance, XC, is equal to the inductive reactance, XL, then the impedance is equal to R. Impedance is equal to where R is the resistance of the resistor, XL is the inductive reactance, and XC is the capacitive reactance. If XL = XC, then (XLXC)2 = 0 and .

When XL = XC and the impedance is equal to R, we say that the R-L-C circuit is in resonance. When a circuit is in resonance, the impedance is a minimum value and the rms current is a maximum value. Resonance occurs at one special AC source angular frequency called the resonant frequency.

This R-L-C series circuit will be in resonance when the angular frequency is . When XL = XC and the impedance is equal to R, we say that the R-L-C circuit is in resonance. Resonance occurs at one special AC source angular frequency called the resonant frequency. To determine this frequency, you can equate XL to XC : and solve for .

When this series R-L-C series circuit is in resonance, the average power loss in the circuit is a maximum value. When a circuit is in resonance, the impedance is a minimum value and the rms current is a maximum value. Since the power loss in the resistor is calculated with P = I2R, a maximum current results in maximum power loss in the resistor.

Discuss!

An RLC circuit is used in a radio to tune into an FM station broadcasting at f = 99.7 MHz. The resistance in the circuit is R = 17.0 Ω, and the inductance is L = 1.10 μH. What capacitance should be used?