An AC series circuit contains a resistor of 20 Ω,an inductor of 50 mH,and a variable capacitor.If the frequency of the applied voltage is 500 Hz,to what setting should the capacitor be set if resonance is achieved?
A) 2.4 µF
B) 3.4 µF
C) 2.0 µF
D) 0.8 µF

Question

Quizplus · Accepted Answer

At resonance, the reactance of the inductor will be equal and opposite to the reactance of the capacitor. 
The reactance of the inductor XL = 2πfL = 2π(500)(0.05) = 31.4 Ω
The reactance of the capacitor Xc = 1/(2πfC) 
At resonance Xc = XL = 31.4 Ω
Substituting f = 500 Hz and XL = Xc = 31.4 Ω we get, 
31.4 = 1/(2π(500)C)
Solving for C, we get C = 2.02 µF which is closest to choice C) 2.0 µF.

An AC Series Circuit Contains a Resistor of 20 Ω,An