As frequency is varied in an RLC series circuit, resonance is reached when
A) the impedance becomes zero.
B) the inductive reactance is equal to the capacitive reactance.
C) the sum of the inductive and capacitive reactances is equal to the resistance.
D) the capacitive reactance is equal to the resistance.
E) the inductive reactance is equal to the resistance.

Question

Quizplus · Accepted Answer

The resonance frequency is the frequency at which the inductive reactance (XL) equals the capacitive reactance (XC), therefore the net reactance (XL-XC) becomes zero, resulting in the minimum impedance. The equations for XL and XC are XL = 2πfL and XC = 1/(2πfC), where f is the frequency, L is the inductance and C is the capacitance of the circuit. At resonance, XL = XC, which implies 2πfL = 1/(2πfC). Therefore, the resonance frequency fr is given by fr = 1/(2π√(LC)), which can be derived by equating XL and XC and solving for f.

As Frequency Is Varied in an RLC Series Circuit, Resonance