A series circuit has an impedance of `60.0 Omega` and a power factor of `0.720` at `50.0 Hz`. The source voltage lags the current.
(a) What circuit element, an inductor or a capacitor, should be placed in series with the circuit to raise its power factor?
(b) What size element will raise the power factor to unity?

Answer

A, B, C, D

Explanation

(a) Voltage lags
`:. X_CgtX_L`
Power factor, `cosphi=R/Z`
`=R/(sqrt(R^2(X_C-X_L)^2)`
To increase the power factor denominator should decrease. Hence `X_L` should increase. Therefore, an inductor is required to be connected.
(b) `cosphi=R/Z=0.72`
`:. R=0.72Z=0.72xx60`
`=43.2Omega`
`(X_C-X_L)=sqrt((60)^2-(43.2)^(2))`
`=41.64Omega`
New inductor of inductane `41.64Omega` should be added in the circuit.
`L=X_L/(2pif)`
`=41.64/(2pi(50))=0.133H`.