In the circuit shown below, the ac source has voltage V=20 (ω t)...

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 In the circuit shown below, the ac source has voltage V=20 (ω t) volt with ω=2000 rad / s The amplitude of the current

In the circuit shown below, the ac source has voltage V=20 (ω t) volt with ω=2000 rad / s The amplitude of the current

Options

A $2 \mathrm{ A}$
B $3.3 \mathrm{ A}$
C $2 / \sqrt{5} \mathrm{ A}$
D $\sqrt{5} \mathrm{ A}$

Correct answer

A. $2 \mathrm{ A}$

Step-by-step solution

\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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