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

Question

Quizplus · Accepted Answer

At resonance, the impedance of the circuit is purely resistive, and the impedance is equal to the resistance. 
$$Z=R=400\ \Omega$$
The resonant frequency is given by:
$$f_0=\frac{1}{2\pi\sqrt{LC}}$$
Substituting the given values,
$$30.0	imes 10^3= \frac{1}{2\pi\sqrt{(2.50	imes 10^{-3})(C)}}$$
Solving for C,
$$C=\frac{1}{(30.0	imes 10^3)^2(2\pi)^2(2.50	imes 10^{-3})}=26.8\ \mu F$$
At resonance, the voltage across the resistor is in phase with the current, and the rms current is given by:
$$I_{rms}=\frac{V_{rms}}{R}=\frac{20\ mV}{400\ \Omega}=50\ \mu A = 50\ \mu F\cdot A$$
Therefore, the answer is D.

An RLC Series Circuit Has a 400 Ω\OmegaΩ Resistance,a 2 μ\muμ A B) 40

An RLC Series Circuit Has a 400 $\Omega$ Resistance,a 2 $\mu$ A
B) 40