A capacitor is connected to an ac generator oscillating at a frequency of 120 Hz

Question

A capacitor is connected to an ac generator oscillating at a frequency of 120 Hz with a maximum voltage of 450 V. The capacitive reactance of the capacitor at this frequency is 240 ?.

What is the capacitance of the capacitor?

A) 5.5 x 10^-6 F

B) 3.5 x 10^-5 F

C) 2.2 x 10^-4 F

D) 2.9 x 10^4 F

E) 1.8 x 10^5 F

What is the rms current in the circuit?

A) 0.53 A

B) 0.75 A

C) 1.3 A

D) 1.9 A

E) 2.7 A

If the frequency of the ac generator is increased from 120 Hz, what will happen to the rms current in the circuit?

A) The rms current keeps increasing.

B) The rms current keeps decreasing.

C) The rms current stays the same.

D) The rms current increases to a maximum value, and then decreases.

E) The rms current decreases to a minimum value, and then increases.

Explanation / Answer

part 1:

capacitive reactance=1/(2*pi*f*C)

=>240=1/(2*pi*120*C)

==>C=1/(2*pi*120*240)=5.5262 uF

hence option A is correct.

part 2:

rms voltage=maximum voltage/sqrt(2)
rms current=rms voltage/capacitive reactance

=(450/sqrt(2))/240=1.3258 A

hence option C is correct.

part 3:

as capacitive reactance is inversely proportional to frequency, if frequency is increased,

reactance will decrease.

as current=voltage/reactance, as reactance decreases, current will increase.

hence option A is correct.

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