Question

In the series $LCR$ circuit shown, the readings of voltmeter and ammeter respectively are

• A. $V=100\text{V};I=2\text{A}$
• B. $V=300\text{V};I=1\text{A}$
• C. $V=1000\text{V};I=2\text{A}$
• D. $V=100\text{V};I=5\text{A}$

Answer 1

The correct option is A $V=100\text{V};I=2\text{A}$


Clearly , $V_L-V_C=0$

$\Rightarrow$ The circuit is in Resonance.

$\therefore$ Impedance of the circuit,
$Z=R=50\Omega$

Now, the reading of voltmeter

$V_{source}=\sqrt{V_R^2+(V_L-V_C{)}^2}$

$V_{source}=\sqrt{V^2+(400-400{)}^2}$

$\Rightarrow V=V_{source}=100\text{V}$

According to ohm's Law:

$\Delta V=iR$

$\Rightarrow i=\frac{\Delta V}{R}=\frac{100}{50}=2\text{A}$

Hence, option $\left(\text{A}\right)$ is correct.