An AC generator with an output rms voltage of 42 V at a frequency of 50 Hz is co

Question

An AC generator with an output rms voltage of 42 V at a frequency of 50 Hz is connected across a 6 µF capacitor. Find the following.
(a) capacitive reactance
____________O

(b) rms current
___________A

(c) maximum current in the circuit
______________A

(d) When does the capacitor have its maximum charge?

a.1/2 cycle before the voltage reaches its maximum value
b.1/4 cycle before the voltage reaches its maximum value
c. 1/3 cycle before the voltage reaches its maximum value when the current takes its maximum value
d.the capacitor's charge is uniform

Explanation / Answer

Part A)

Xc = 1/2fC = 1/(2)(50)(6 X 10-6)

Xc = 530.5

Part B)

The rms current is found by

Vrms = IrmsXc

Irms = (Vrms/Xc) = (42/530.5)

Irms = .079 A

Part C)

Imax = 2(Irms)

Imax = .112 A

Part D)

The voltage always lags behind the current by 1/4 of a cycle in a capacitave circuit.

That means the charge will lead the voltage by 1/4 of a cycle. The answer is B

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