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An inductor of reactance 1 Omegaand a re...

An 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
Average power dissipated in the circuit ,
`lt P gt =V_"rms" I_"rms" cos phi` …(1)
but `I_(rms)=V_(rms)/Z`
but `Z=sqrt(R^2+X_L^2)=sqrt((2)^2 + (1)^2)=sqrt5Omega`
`therefore I_(rms)=V_(rms)/Z=6/sqrt5`A ….(2)
cos `phi=R/Z=2/sqrt5`...(3)
Putting the values of equation (2) and (3) in equation (1),
`lt P gt =6xx6/sqrt5xx2/sqrt5`
`=72/5`
`therefore lt P gt` =14.4 W
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