Question

In the circuit shown below, the ac source has voltage$V=20\cos \left(\omega t\right)$ volts with $\omega =200rad/sec$. the amplitude of the current will be nearest to

• A. $\frac{2}{\sqrt{5}}A$
• B. $2A$
• C. $3.3A$
• D. $\sqrt{5}A$

Answer 1

The correct option is B $2A$

$Z=\sqrt{(R^2+(X_L-X_C{)}^2}$

Given $L=5\times {10}^{-3}H,C=50\times {10}^{-6}F,\omega =200rads{s}^{-1}$

Here $R=6\Omega +4\Omega =10\Omega$

$X_L=L\omega =(5\times {10}^{-3})\left(2000\right)=10\Omega$
And
$X_C=\frac{1}{\omega C}=\frac{1}{\left(2000\right)(50\times {10}^{-6})}=10\Omega$

$Z=\sqrt{(10{)}^2+(10-10{)}^2}$
$Z=10\Omega$
$i=V_0/Z$
Here $V=20\cos \left(\omega t\right)\Rightarrow V_0=20V$
$i=\frac{20}{10}=2A$
Hence, the correct option is $\left(A\right)$.