Question

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

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

Answer 1

The correct option is C $14.4W$

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