Question

In the circuit shown in figure, $AC$ source gives a voltage $V=20\cos 2000t$. Neglecting source resistance, ammeter readings will be

• A. $2.5\text{A}$
• B. $1.4\text{A}$
• C. $1.6\text{A}$
• D. $2.0\text{A}$

Answer 1

The correct option is B $1.4\text{A}$

Given, $E=20\cos 2000t$

Comparing above equation with $E=E_0\cos \omega t$ , we get

$E_0=20\text{V}$ and $\omega =2000\text{rad/sec}$

Here, Ammeter reads the source current which is

$I=\frac{(V_{rms}{)}_{source}}{Z}$

Where, $Z^2=R_{eq}^2+(X_L-X_C{)}^2$

$X_L=\omega L=2000\times 5\times {10}^{-3}=10\Omega$

$X_C=\frac{1}{\omega C}=\frac{1}{2000\times 50\times {10}^{-6}}=10\Omega$

$=(6+4{)}^2+{(10-10)}^2={10}^2$

$\Rightarrow Z=10\Omega$

So, $I=\frac{(E_{rms}{)}_{source}}{Z}=\frac{20}{\sqrt{2}\times 10}=\sqrt{2}$

$\Rightarrow I=1.414\text{A}$