In the given circuit, rms value of current ( I _ rms ) through the...

In the given circuit, $rms$ value of current $\left({I}_{rms}\right)$ through the resistor $R$ is :

In the given circuit, rms value of current ( I _ rms ) through the resistor R is :

Options

A $2A$
B $\dfrac{1}{2}A$
C $20A$
D $2\sqrt{2}A$

Correct answer

A. $2A$

Step-by-step solution

In the given circuit, rms value of current ( I _ rms ) through the resistor R is :

Impedance of the given LCR circuit will be, $Z = \sqrt{{R}^{2} + {\left({X}_{L} - {X}_{C}\right)}^{2}} ⇒ Z = \sqrt{{100}^{2} + {\left(200 - 100\right)}^{2}}$

$= 100\sqrt{2}Ω$

Therefore, RMS current can be written as,

${I}_{rms} = \dfrac{{V}_{rms}}{Z} = \dfrac{200\sqrt{2}}{100\sqrt{2}}$

$= 2A$

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