An AC series circuit contains a resistor of 10 Ω,a capacitor of 1.20 μF and an inductor of 110 mH.What frequency should be used to create a resonance condition in the circuit?
A) 139 Hz
B) 1210 Hz
C) 1100 Hz
D) 438 Hz
E) 877 Hz

Question

An AC series circuit contains a resistor of 10 Ω,a capacitor of 1.20 μF and an inductor of 110 mH.What frequency should be used to create a resonance condition in the circuit?
A) 139 Hz
B) 1210 Hz
C) 1100 Hz
D) 438 Hz
E) ​877 Hz

Quizplus · Accepted Answer

Resonance occurs in an AC series circuit when the capacitive reactance (Xc) equals the inductive reactance (Xl):
Xc = 1/2πfC and Xl = 2πfL

At resonance: Xc = Xl
1/2πfC = 2πfL
f = 1 / 2π √(LC)

Substituting the given values: 
f = 1 / 2π √(110mH * 1.20μF)
f = 437.8 Hz ≈ 438 Hz

Therefore, the frequency that should be used to create a resonance condition in the circuit is 438 Hz, which is option D).

An AC Series Circuit Contains a Resistor of 10 Ω,A