A 10.0-μF capacitor is plugged into a 110 V-rms 60.0-Hz voltage source, with an ammeter in series. What is the rms value of the current through the capacitor?
A) 0.202 A (rms)
B) 0.415 A (rms)
C) 0.626 A (rms)
D) 0.838 A (rms)
E) 0.066 A (rms)

Question

Quizplus · Accepted Answer

The capacitive reactance XC, in ohms, is given by XC = 1/(2πfC), where f is the frequency in Hz and C is the capacitance in farads. Plugging in the given values, XC = 1/(2π(60)(10.0×10^-6)) = 265.26 ohms. The current through the capacitor is given by I = V/XC, where V is the voltage across the capacitor. Since the voltage source is rms, V = 110 V / √2 = 77.942 V (peak voltage). Therefore, I = 77.942 V / 265.26 ohms = 0.294 A (peak current). The rms value of the current is then given by Irms = I / √2 = 0.294 A / √2 = 0.415 A (rms), which is closest to choice B.

A 100-μF Capacitor Is Plugged into a 110 V-Rms 60