The r.m.s. current in an A.C. circuit is 4A. If the wattless current `2 sqrt(3)A`, then the power factor of the circuit is

Options

A. a. `1/3`
B. b. `1/2`
C. c. `1(sqrt(2))`
D. d. `sqrt(3)`

Answer

B

Explanation

`OM = I_(rms) xx cos theta`. This contributes for power.
`PM = I_(rms) xx sin theta`. This does not contribute for power.
Hence it is wattless.
`:. I_("wattless") = I_(rms) xx sin theta`
`:. 2sqrt(3) = (sqrt3)/2`
`:. theta = 60^(@)`
`:.` Power factor = cos theta = cos 60^(@) = 1/2`.