In a series LCR circuit shown below the power factor is unity . Calculate the capacitance C of the capacitor.

Explanation

Power factor the circuit is given by
cos `Phi= (R )/(Z ) =1 :. Z =R `
where Z is the impedance of the circuit
`:. X_(C) = X_(L) or (1)/(2pifc)= 2pifL`
Here `f = 50 s^(-1)`
`implies C = (1)/(4pi^(2)f^(2)L)`
`= (1)/(4xx(3.14)^(2)xx(50)^(2)xx100xx10^(-3))`
`= 100 mu F `