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A inductor of reactance 1 Omega and a re...

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

A

8 W

B

12 W

C

14.4 W

D

18 W

Text Solution

Verified by Experts

The correct Answer is:
C
Given , `X_L = 1Omega` , R `= 2Omega`
`E_rms = 6 V , P_av = ?`
Average power dissipated in the circuit
`P_av = V_rms I_rms cos phi`
`I_rms = I_o/ sqrt 2 = V_rms/Z`
Z = `sqrt R^(2) + X_L^(2)`
`sqrt 4 + 1` = `sqrt 5`
`I_rms = 6/sqrt 5A`
`cos phi = R/Z = 2/sqrt 5`
`P_av = 6 xx 6/sqrt 5 xx 2 / sqrt 3` [from Eq.(i)]
`= 72/sqrt 5sqrt 5 = 72/5 = 14.4` W
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