A coil of inductive reactance `31 Omega` has a resistance of `8 omega`. 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. `0.56`
B. `0.64`
C. `0.80`
D. `0.33`

Answer

C

Explanation

Power factor `(cos phi)` is a ratio fo resistance and impedence of `AC` circuit. Power factor of `AC` circuit is given by
`cos phi=R/Z......(i)`
Where `R` is resistance employed and `Z` the impedence of the circuit.
`Z=sqrt(R^(2)+(X_(L)-X_(C)^(2)))........(ii)`
Eqs (i) and (ii) meet to give,
`cos phi=R/(sqrt(R^(2)+(X_(L)-X_(C))^(2)))........(iii)`
Given, `R=8 Omega, X_(L)=21Omega, X_(C)=25 Omega`
`cos phi=8/(sqrt((8)^(2)+(31-25)^(2)))=8/(sqrt(64+36))`
`cos phi=0.80`