A series RLC circuit has a capacitive reactance of 16 Ω and an inductive reactance of 4.0 Ω at 30 Hz. What frequency would result in resonance for this circuit?
A) 12 Hz
B) 60 Hz
C) 15 Hz
D) 7.5 Hz
E) Resonance is not possible in this case.

Question

Quizplus · Accepted Answer

Resonance occurs when the capacitive reactance and inductive reactance are equal in magnitude and opposite in sign. This happens when:

1/(2*pi*f*C) = 2*pi*f*L

Simplifying this equation, we get:

f^2 = 1/(2*pi*C*L)

Plugging in the given values, we get:

f^2 = 1/(2*pi*16*4)

f^2 = 0.003125

f = 0.056 Hz

So the frequency of resonance is approximately 56 Hz. However, this is not one of the given answer choices. The closest answer choice is B, 60 Hz.

A Series RLC Circuit Has a Capacitive Reactance of 16