If for above circuit the capacitive reactance is two times of inductive Reactance, and resistance R is equal to inductance Reactance then power factor of circuit is .

Options

A. 1
B. zero
C. `(1)/(2)`
D. `(2)/(sqrt(5))`

Answer

D

Explanation

`X_(X)=2X_(L)=2R`
`(1)/(z^(2))=(1)/(R^(2))+((1)/(X_(L))-(1)/(X_(C)))^(2)`
`=(1)/(R^(2))+((1)/(2R)-(1)/(R))^(2)=(5)/(4R^(2))z=(2R)/(sqrt(5))`
power factor in parallel combination
`= cos theta = (z)/(R)=(2)/(sqrt(5))`
Alternate solution :

`cos phi=(I)/(sqrt(I^(2)+(I^(2))/(4))+(2)/(sqrt(5)))`.