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In the circuit shown below, the ac source has voltage $V=20 \cos (\omega t)$ volt with $\omega=2000 \mathrm{rad} / \mathrm{s}$
The amplitude of the current will be nearest to
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The amplitude of the current will be nearest to
Solution:
1518 Upvotes
Verified Answer
The correct answer is:
$2 \mathrm{~A}$
$$
\begin{aligned}
Z=& \sqrt{R^{2}+\left(\omega L-\frac{1}{\omega C}\right)^{2}} \\
&=\sqrt{10^{2}+\left(2000 \times 5 \times 10^{3}-\frac{1}{2000 \times 50 \times 10^{-6}}\right)^{2}} \\
=& 10 \Omega \\
\quad i=\frac{V_{0}}{Z}=\frac{20}{10}=2 A .
\end{aligned}
$$
\begin{aligned}
Z=& \sqrt{R^{2}+\left(\omega L-\frac{1}{\omega C}\right)^{2}} \\
&=\sqrt{10^{2}+\left(2000 \times 5 \times 10^{3}-\frac{1}{2000 \times 50 \times 10^{-6}}\right)^{2}} \\
=& 10 \Omega \\
\quad i=\frac{V_{0}}{Z}=\frac{20}{10}=2 A .
\end{aligned}
$$
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