Question

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

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

Answer 1

Answer: (C)

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