A resistor of 50Ω , inductor of self inductance ( π 2 3 ) H and a capacitor of unknown capacity are connected in series to an a.c. source of 100 V and 50 Hz . When the voltage and current are in pha

Question

A resistor of 50Ω , inductor of self inductance ( π 2 3 ​ ) H and a capacitor of unknown capacity are connected in series to an a.c. source of 100 V and 50 Hz . When the voltage and current are in phase, the value of capacitance is (nearly)

TestHub · Accepted Answer

When voltage and current are in phase, the circuit is in resonance.

At resonance, $X_{L} = X_{C}$

$ω L = \frac{1}{ω C}$

$C = \frac{1}{ω ^{2} L} = \frac{1}{( 2 π f ) ^{2} L}$

Given $f = 50$ Hz, $L = \frac{3}{π ^{2}}$ H

$C = \frac{1}{( 2 π \times 50 ) ^{2} \times ( \frac{3}{π ^{2}} )}$

$C = \frac{1}{10000 π ^{2} \times \frac{3}{π ^{2}}}$

$C = \frac{1}{30000}$

$C = 0.33 \times 1 0^{- 4}$ F

Answer: $0.33 \times 1 0^{- 4} F$

Physics - Capacitor Question with Solution | TestHub

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