Question

In the given RLC circuit power dissipation if frequency is half of resonant frequency

• A. 80 watt
• B. 50 watt
• C. 40 watt
• D. 20 watt

Answer 1

The correct option is A 80 watt

${\omega }_R=\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{2\times {10}^{-3}\times 5\times {10}^{-6}}}={10}^4$
So $\omega =\frac{{\omega }_R}{2}=5\times {10}^3\Rightarrow X_C=\frac{1}{\omega C}=40\Omega$ and
$X_L=\omega L=10\Omega$
$\therefore Z=\sqrt{R^2+(\omega L-\frac{1}{\omega C}{)}^2}=50\Omega \Rightarrow i_{rms}=\frac{{\epsilon }_{rms}}{Z}=\frac{100}{\sqrt{2}\times 50}=\sqrt{2}A$
$P=i_{rms}^{2}R=2\times 40=80Watt$