Question

An inductor of reactance $60\Omega$, capacitor of reactance $30\Omega$ and resistor of resistance $40\Omega$ are connected in series across a source of emf $V=100\sin 628t$. Find power loss in the circuit.

• A. $80W$
• B. $40W$
• C. $60W$
• D. $120W$

Answer 1

The correct option is A $80W$

We know that
$P_{avg}=V_{rms}{i}_{rms}\cos \varphi$
$P_{avg}=V_{\text{rms}}{i}_{\text{rms}}\left(\frac{R}{Z}\right)$
$=\left(\frac{V_{rms}}{Z}\right)i_{\text{rms}}R=(i_{\text{rms}}{)}^{2}R$
$Z=\sqrt{R^2+(X_L-X_C{)}^2}=\sqrt{{40}^2+(60-30{)}^2}=50\Omega$
$i_{\text{rms}}=\left(\frac{V_{\text{rms}}}{Z}\right)$
$i_{\text{rms}}=\frac{100}{\sqrt{2}\times 50}=\sqrt{2}\text{A}$

$P_{\text{avg}}=i_{rms}^{2}R=2\times 40=80W$