Question

In the circuit shown in the figure, the ac source gives a voltage $V=20\cos \left(2000t\right)$. Neglecting source resistance, the voltmeter and ammeter readings will be

• A. $0\text{V},0.47\text{A}$
• B. $1.68\text{V},0.47\text{A}$
• C. $0\text{V},1.4\text{A}$
• D. $5.6\text{V},1.4\text{A}$

Answer 1

The correct option is D $5.6\text{V},1.4\text{A}$

$Z=\sqrt{(R{)}^2+(X_L-X_C{)}^2}$
$R=10\Omega ,X_L=\omega L=2000\times 5\times {10}^{-3}=10\Omega$
$X_C=\frac{1}{\omega C}=\frac{1}{2000\times 50\times {10}^{-6}}=10\Omega$
i.e., $Z=10\Omega$
Maximum current $i_0=\frac{V_0}{Z}=\frac{20}{10}=2\text{A}$
Hence, $i_{\text{rms}}=\frac{2}{\sqrt{2}}=1.4\text{A}$
and $V_{\text{rms}}=4\times 1.41=5.64\text{V}$
Voltmeter's reading will be
$V_{\text{rms}}=i_{\text{rms}}.R$
$=1.4\times 4=5.6\text{Volt}$