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

Answer 1

Answer: (B)

$0.79$ W

$L=20mH$ $C=100\mu F$ $R=50\Omega$

$V=10sin\left(314t\right)$

$V_0=10$, $\omega =314$

$X_L=wL=314\times 20\times {10}^{-3}=6.28\Omega$

$X_C=\frac{1}{\omega C}=31.8\Omega$

$Z=\sqrt{R^2+(X_C-X_L{)}^2}=56.1$

$PowerlossP=\frac{V_0^{2}R}{2Z^2}=0.79W$