A 120-V rms voltage at 60 Hz is applied across an RC circuit. The rms value of the current in the circuit is 0.60 A and it leads the voltage by 60°. What is the value of the capacitance in this circuit?
A) 13 μF
B) 14 μF
C) 15 μF
D) 16 μF
E) 17 μF

Question

Quizplus · Accepted Answer

We know that the rms current is given by:

$I_{rms}=\frac{V_{rms}}{Z}$

where Z is the impedance of the circuit. In an RC circuit, impedance is given by:

$Z=\sqrt{R^2+\frac{1}{\omega^2C^2}}$

where R is the resistance, C is the capacitance, and $\omega=2\pi f$ is the angular frequency.

Since we know the rms voltage and current, we can calculate the impedance:

$0.60=\frac{120}{\sqrt{R^2+\frac{1}{(2\pi	imes60	imes C)^2}}}$

Solving for C, we get:

$C\approx 15\,\mu F$

Therefore, the best choice is C, 15 μF.

A 120-V Rms Voltage at 60 Hz Is Applied Across