An RLC series circuit has a 400 Ω resistance, a 2.50 mH inductor, and a capacitor. If the resonant frequency is 30.0 kHz, and the circuit is attached to a 20 mV rms power supply, what is the rms current at resonance?
A) 60 μA
B) 40 μA
C) 30 μA
D) 50 μA
E) 25 μA

Question

Quizplus · Accepted Answer

The resonant frequency can be calculated using the formula: 
f = 1/2π√(LC)

Where L is the inductance and C is the capacitance.

Given: 
R = 400 Ω
L = 2.50 mH = 0.00250 H
f = 30.0 kHz

We can rearrange the formula to solve for capacitance:

C = 1/((2πf)^2L)

C = 1/((2π × 30.0 kHz)^2 × 0.00250 H) ≈ 51.9 nF

The impedance of the circuit can be calculated as:

Z = √(R^2 + (ωL - 1/ωC)^2)

At resonance, ωL = 1/ωC, so the equation becomes:

Z = R

Therefore, the rms current at resonance can be calculated as:

I = V/R = 20 mV / 400 Ω = 50 μA

So, the correct choice is D.

An RLC Series Circuit Has a 400 Ω Resistance, a 2.50