In the circuit, as shown in the figure, if the value of `R.M.S` current is 2.2 ampere, the power factor of the box is `(E = 220 V)`

Options

A. `(1)/(sqrt(2))`
B. 1
C. `(sqrt(3))/(3)`
D. `(1)/(2)`

Answer

A

Explanation

`Z = (220)/(2.2) = 100, R = Z`
`X_(c ) = X_(L) = 100 pi xx (1)/(pi) = 100`
Power factor of box
`= (R )/(sqrt(R^(2) + X_(C )^(2))) = (100)/(sqrt(100^(2) + 100^(2))) = (1)/(sqrt(2))`