Question

An inductor of reactance 1 Ω and a resistor of 2 Ω are connected in series to the terminals of a 6 V (rms) AC source. The power dissipated in the circuit is ______.

Options

• 8 W

• 12 W

• 14.4 W

• 18 W

Answer 1

An inductor of reactance 1 Ω and a resistor of 2 Ω are connected in series to the terminals of a 6 V (rms) AC source. The power dissipated in the circuit is 14.4 W.

Explanation:

Here V_rms = 6V, X_L = 1Ω, R = 2Ω, P_av =?

Since, average power dissipated in the circuit is given by,

P_av = V_rms I_rms cos Φ

\[I_{\mathrm{rms}}=\frac{I_{0}}{\sqrt{2}}=\frac{V_{rms}}{Z}\]

Z = \[\sqrt{R^2+X_{L}^2}=\sqrt{4+1}=\sqrt{5}\Omega\]

\[\therefore\] I_rms = \[\frac {6}{\sqrt 5}\]A

\[\cos\phi=\frac{R}{Z}=\frac{2}{\sqrt{5}}\]

\[P_{av}=6\times\frac{6}{\sqrt{5}}\times\frac{2}{\sqrt{5}}=14.4W\]