A coil of inductive reactance `31 Omega` has a resistance of `8 ohm`. It is placed in series with a condenser of capacitive reactance `25 Omega`. The combination is connected to an `ac` source of `110 V`. The power factor of the circuit is

Options

A. `0.80`
B. `0.33`
C. `0.56`
D. `0.64`

Answer

A

Explanation

`X_(L) = 31 Omega , R = 8 Omega , X_(C) =25 Omega `
`Z = sqrt(R^(2) + (X_(L) - X_(C))^(2)) = sqrt((8)^(2) + (31 - 25)^(2) = 10Omega)`
power factor `cos phi = R/(Z) = (8)/(10) = 0.8` .