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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:
3
Here, `X_(L) = 1 Omega, R = 2 Omega, V_("rms") = 6 V`
Impedance of the circuit
`Z = sqrt(X_(L)^(2) + R^(2)) = sqrt((1)^(2) + (2)^(2))= sqrt(5) Omega`
`I_("rms") = (V_("rms"))/(Z) = (6)/(sqrt(5)) A`
Power dissipated
`P = V_("rms") I_("rms") cos phi = V_("rms") I_("rms") (R )/(Z)`
`= 6 xx (6)/(sqrt(5)) xx (2)/(sqrt(5)) = (72)/(5) = 14.4 W`
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