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)/(sqrt5)`

Explanation

`X_(C)=2X_(L)=2R`
`(1)/(Z^(2))=(1)/(R^(2))+((1)/(X_(L))-(1)/(X_(C)))=(1)/(R^(2))+((1)/(2R)+(1)/(R))^(2)=(5)/(4R^(2))`
`z=(2R)/(sqrt5)`
Power factor is parallel combination=`cos theta=(z)/(R)=(2)/(sqrt5)`