Question

A 100μF capacitor is connected across 220V, 50 Hz source. Calculate the reactance offered by the capacitor at fundamental and 140 Hz frequency, maximum current in the circuit, the average and r.m.s. value of the current drawn by the capacitor.

Answer 1

Given : Capacitance, C = 100μF, maximum voltage, V = 220 V, fundamental frequency, F° = 50 Hz, another frequency, F = 140 Hz

To find : Reactance offered by the capacitor at fundamental and 140 Hz frequency, maximum current in the circuit, the average and r.m.s. value of the current drawn by the capacitor.

Solution : We know that,

Capacitor reactance = 1/wC

• Reactance due to fundamental frequency,

X = 1/wC = 1/2πF°×C

X = 1/2×π×50×100×$10{}^{-6}$

= 100×7/22

X = 50×7/11

X = 31.81

• Reactance due to another frequency,

P = 1/2π×140×100×$10{}^{-6}$

= 1000/88

P = 250/22

P = 11.36

• Maximum current, Io = V/X

Io = 220×11/50×7

Io = 6.91 A

• Average current, I = Io/π

I = 220×11×7/50×7×22

I = 10×11/50

= 11/5

I = 2.2 A

• R.M.S value of current, I° = Io/$2{}^{1/2}$

I° = 220×11/50×7×1.414

I° = 4.88 A

• Reactance offered by the capacitor at fundamental and 140 Hz frequency, maximum current in the circuit, the average and r.m.s. value of the current drawn by the capacitor is 31.81, 11.36, 6.91 A, 2.2 A and 4.88 A respectively.