Find the capacity of a capacitor, which when put in series with a 10 ohm resistor, makes the power factor equal to 0.5. Assume an 80 V - 100 Hz a.c. supply.

Explanation

Here, `C = ?, R = 10 ohm , cos phi = 0.5`,
`E_(v) = 80 V, v = 100 hz`
As `cos phi = (R )/(Z) , Z = (R )/(cos phi) = (10)/(0.5) = 20`
As `R^(2) + X_(C )^(2) = Z^(2)`
`:. X_(C ) = sqrt(Z^(2) - R^(2)) = sqrt(20^(2) - 10^(2)) = 10 sqrt3`
`(1)/(omega C) = 10 sqrt3, C = (1)/(omega 10 sqrt3) = (1)/(2 pi xx 100 xx 10 sqrt3`
`= 9.2 xx 10^(-5) F`