In the circuit shown in fin. Calculate the capacitance C of the capacitor, if the power factor of the circuit is unity. Also, calculate Q factor of the circuit.

Explanation

Here, `C = ?`,
Power factor, `cos phi = (R )/(Z) = 1`
`:. Z = R :. X_(C ) = X_(L) , (1)/(2 pi v C) = 2 pi v L`
`C = (1)/(4 pi^(2) v^(2) L) = (1)/(4(3.14)^(2) (50)^(2) xx 200 xx 10^(-3))`
`= 5 xx 10^(-5) f = 50 mu F`
Q factor `= (1)/(2) sqrt((L)/(C)) = (1)/(10) sqrt((200 xx 10^(-3))/(50 xx 10^(-6))) = 6.32`