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. 0.4
B. 0.64
C. 0.8
D. 0.32

Answer

C

Explanation

Power factor
`= cos phi (X_(L) = 31 Omega, X_(C) = 25 Omega and R = 8Omega)`
`=(R)/(sqrt(R^(2)+(X_(L)-X_(C))^(2)))`
`=(R)/(sqrt(64+(31-25)^(2)))`
`:. cos phi = 8/(sqrt(64+36)) = 8/10 = 0.8`.