Question

A $100volt$ $AC$ source of angular frequancy $500rad/s$ is connected to a $LCR$ circuit with $L=0.8H$, $C=5\mu F$ and $R=10\Omega$, all connected in series. The potential difference across the resistance is

• A. $\frac{100}{\sqrt{2}}volt$
• B. $100volt$
• C. $50volt$
• D. $50\sqrt{3}$

Answer 1

The correct option is B $100volt$

The impedance of LCR circuit is given as,

$Z=\sqrt{\left[R^2+{\left(\omega L-\frac{1}{\omega C}\right)}^2\right]}$

$=\sqrt{{\left(10\right)}^2+\left(\left(2\times \pi \times 500\times 8.1\times {10}^{-3}\right)-\frac{1}{2\times \pi \times 500\times 12.5\times {10}^{-6}}\right)}$

$=10ohm$

The rms value of the current is given as,

$I_{rms}=\frac{V_{rms}}{Z}$

$=\frac{100}{10}$

$=10A$

The potential difference across the given resistor is given as,

$V_R=I\times R$

$=10\times 10$

$=100V$

Thus, the potential difference across the resistor is $100V$.