Question

In the circuit shown below, the ac source has voltage $V=20 \, \cos (\omega t)$ volts with $\omega=2000 \,rad / sec$. The amplitude of the current will be nearest to

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

Answer 1

Answer: (A)

$R=6+4=10 \,\Omega$
$ 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 $
$\therefore Z =\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}=10\, \Omega$
Amplitude of current $=i_{0}=\frac{V_{0}}{Z}=\frac{20}{10}=2 \,A$