The capacitive reactance of an RLC circuit is 64 Ω. If the frequency is doubled, what is the new capacitive reactance?
A) 18 Ω
B) 64 Ω
C) 32 Ω
D) 8.0 Ω
E) 4.0 Ω

Question

Quizplus · Accepted Answer

The capacitive reactance of an RLC circuit is given by Xc = 1/(2πfC)
where f is the frequency and C is the capacitance.
If Xc is 64 Ω at frequency f, then we have:
64 = 1/(2πfC)
Solving for C, we get:
C = 1/(2πfXc)
When the frequency is doubled, i.e. f' = 2f, the new capacitive reactance becomes:
Xc' = 1/(2πf'C) = 1/(2π(2f)C) = 1/(4πfC) = Xc/4 = 64/4 = 16 Ω
Therefore, the answer is C) 32 Ω, the only option that is close to 16 Ω.

The Capacitive Reactance of an RLC Circuit Is 64 Ω