Question

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

• A. 0 V, 0.47 A
• B. 1.68 V, 0.47 A
• C. 0 V, 1.4 A
• D. $2\sqrt{2}v,\sqrt{2}A$

Answer 1

Answer: (D)

Z = $\sqrt{R^2+(X_L-X_C{)}^2}$
Here $R=6+4=10\Omega$, $\omega =2000rd{s}^{-1}{X}_L=\omega L=2000\times 5\times 10^{-3}=10\Omega$ and
$X_C=\frac{1}{{\omega }_C}=\frac{1}{200\times 50\times 10^{-6}}=10\Omega$
$Z=\sqrt{10^2+(10-10{)}^2}=10\Omega$
Current , $I_o=\frac{V_o}{Z}=\frac{20}{10}=2A\therefore I_{rms}=\frac{2}{\sqrt{2}}=\sqrt{2}A$
Voltage $V=\sqrt{2}\times \sqrt{4^2+0}+2\sqrt{2}V$