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. 12 W
C. 14.4 W
D. 18 W

Answer

C

Explanation

Given, `X_(L)=1Omega, R=2Omega`
`E_(rms) = 6V, P_(av)=?`
Average power dissipated in the circuit,
`P_(av) = E_(rms) I_(rms) cosphi`...........(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`
`cosphi = R/Z=2/sqrt(5)`
`P_(av) = 6 xx 6/sqrt(5) xx 2/sqrt(5)` {from Eq.(i)}
`=72/(sqrt(5)sqrt(5))=73/5=14.4` W