A capacitor of unknown value and an inductor of 0.1H and a resistor of `10Omega`are connectedin series to a 220V, 50Hz ac source. It is foundthat the power factor of circuit is unity.Calculate the capacitance of capacitor and maximum amplitude of current

Explanation

C = ?
L = 0.1H
`R = 10Omega`
Frequency = v = 50 Hz
Power factor = Coses = 1
The power factor of an a.c. circuit is unity, when the circuit is purely resistive i.e. `X_L = X_C`
`implies 2pivL =12pivc`
`C=1/(2pi^2v^2L)`
`=1/(4xx(3.14)^2xx(50)^2xx(0.1)^2)`
`=1/(4xx9.8596xx2500xx10^(-2))`
`=1/(9.8596xx10^2)`
`=0.104xx10^(-2)`
`C = 1.014 xx10^(-3)F`
`C = 1.014 mF`
`C = 1014muF`