A resistor of 100Omega, a pure inductance coil of L=0.5 H and capacitor are in series in a circuit containing an a.c. source of 200 V , 50 Hz . In the circuit , current is ahead of the voltage by 30^@. Find the value of the capacitance.

A resistor of 100Omega, a pure inductance coil of L=0.5 H and capacito

1.	A resistor of 100Omega, a pure inductance coil of L=0.5 H and capacitor are in series in a circuit containing an a.c. source of 200 V , 50 Hz . In the circuit , current is ahead of the voltage by 30^@. Find the value of the capacitance.
Answer» Solution :Here `R=100Omega`, L=0.5 H, C= ? , V=200 V , f=50 HZ, `f=30^@` We have, `TAN phi=(X_C-X_L)/R` `tan 30^@ =(X_C-X_L)/100 "" because X_L=omegaL` & `X_C=1/(omegaC)` `0.5xx100=1/(2pifC)-2pifL(because omega=2pif)` `0.5xx100=1/(2xx3.14xx50C)-2xx3.14xx50xx0.5` `50=1/(314C)-157` `50+157=1/(314C)` `207=1/(314C)` `C=1/64998=0.00001538` C=15.38 `muF`

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A resistor of 100Omega, a pure inductance coil of L=0.5 H and capacitor are in series in a circuit containing an a.c. source of 200 V , 50 Hz . In the circuit , current is ahead of the voltage by 30^@. Find the value of the capacitance.

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