Question

An inductor $20\, mH$, a capacitor $100\, \mu F$ and a resistor $50 \, \Omega$ are connected in series across a source of emf, $V\, = \,10 \,sin\, 314\, t$. The power loss in the circuit is

• A. 1.13 W
• B. 0.79 W
• C. 2.74 W
• D. 0.43 W

Answer 1

Answer: (B)

0.79 W

Answer 2

$P_{av} = \left(\frac{V_{RMS}}{Z}\right)^{2} R$
$Z = \sqrt{R^{2} + \left(\omega L - \frac{1}{\omega C}\right)^{2}} = 56\, \Omega$
$\therefore P_{av} = \left(\frac{10}{\left(\sqrt{2}\right)56}\right)^{2} \times50 = 0.79 \,W$