When an inductor L and a resistor R in series are connected across a 12 v, 50 Hz supply a current of 0.5 A flows in the circuit . The current differs in the phase from applied voltage by `(pi)/(3)` radian . Then the value of R is

Options

A. `10 Sigma`
B. `3 Sigma`
C. `12 Sigma`
D. `15 Sigma`

Answer

C

Explanation

Given situation following the fitgure below

Given for Ac circuit
`V_(ms ) = 12 V`
Frequency `f= 50 Hz`
current `I = 0.5 A`
phase difference `phi = (pi )/( 3 )`
`:. ` Impedance of the AC circuit
`Z = (V_(nms) )/(I ) = (12)/( 0.5 ) rArr Z = 24 Sigma `
Power factor
`rArr cos phi = (R )/(2) rArr cos (pi )/(3 ) = (R )/( 24) rArr (1)/(2) = (R )/(24 ) rArr R = 12 Sigma `