A inductor of reactance `1 Omega` and a resistor of `2 Omega` are connected in series to the terminals of a 6 V (rms) a.c. source. The power dissipated in the circuit is

Options

A. 8W
B. 12W
C. 14 4. W
D. 18W

Answer

C

Explanation

Given , `X_(L) = 1 Omega , R = 2 Omega `
`E_(rms) = 6 V , P_(av) = ?`
Average power dissipated in the circuit
`P_(av) = E_(rms)I_(rms) cos phi" "` . . . (i)
`I_(rms) = (I_(0))/(sqrt(2)) = (E_(rms))/(Z)`
`Z = sqrt(R^(2) + X_(L)^(2))`
`= sqrt(4 + 1) = sqrt(5)`
`I_(rms) = (6)/(sqrt(5)) A `
`cos phi = (R)/(Z) = (2)/(sqrt(5))`
`P_(av) = 6 xx (6)/( sqrt(5)) xx (2)/( sqrt(5)) " "` [ fromEq. (i) ]
`=- (72)/( sqrt(5)sqrt(5)) = (72)/(5) = 14.4 W `