Question

An inductor of reactance $1\,\Omega$ and a resistor of $2\,\Omega$ are connected in series to the terminals of a $6\, V\,(rms)$ ac source. The power dissipated in the circuit is

• A. $8\,W$
• B. $12\,W$
• C. $14.4\,W$
• D. $18\,W$

Answer 1

Answer: (C)

Here, $X_L= 1\,\Omega$,
$R=2\,\Omega$,
$V_{rms}=6\,V$
Impedance of the circuit
$Z=\sqrt{X^{2}_{L}+R^{2}}$
$=\sqrt{\left(1\right)^{2}+\left(2\right)^{2}}$
$=\sqrt{5}\,\Omega$
$I_{rms}=\frac{V_{rms}}{Z}$
$=\frac{6}{\sqrt{5}}\,A$
Power dissipated
$P=V_{rms}\,I_{rms}\,cos\,\phi=V_{rms}\,I_{rms} \frac{R}{Z}$
$=6 \times\frac{6}{\sqrt{5}} \times \frac{2}{\sqrt{5}}=\frac{72}{5} $
$=14.4\,W$