Question

In a given R-L-C circuit where $R=30\Omega$
$L=20mHandC=\frac{50}{3}\mu F$

• A. reading of Ammeter is $\frac{2}{5}A$
• B. reading of voltmeter $V_1$ is $6\sqrt{10}V$
• C. reading of voltmeter $V_2$ is 8V
• D. potential difference across AB can be greater than 20V at an instant.

Answer 1

Answer: (B), (D)

potential difference across AB can be greater than 20V at an instant.

$X_L=\omega L=20\Omega$,
$X_C=\frac{1}{\omega c}=60\Omega$
$z=\sqrt{{30}^2+(60-20{)}^2}=50i=\frac{20\sin \omega t}{50}=\frac{2}{5}\sin \omega t,i_{rms}=\frac{\sqrt{2}}{5}{V}_1=i_{rms}{Z}_1=\frac{\sqrt{2}}{5}\sqrt{{30}^2+{60}^2}=6\sqrt{10}V{V}_2=i_{rms}{Z}_1=\frac{\sqrt{2}}{5}\times 40=8\sqrt{2}{V}_{1max}=V_1\sqrt{2}=6\sqrt{10}\times \sqrt{2}=26.8$
So $V_1$ can take a value of 20 V.