In the given circuit, r.m.s. value of current through the resistor $\mathrm{R}$ is

In the given circuit, r.m.s. value of current through the resistor $\mathrm{R}$ is
  1. $2 \mathrm{~A}$
  2. $0.5 \mathrm{~A}$
  3. $20\mathrm{~A}$
  4. $2 \sqrt{2} \mathrm{~A}$

Solution

$\begin{aligned} \mathrm{Z} & =\sqrt{\mathrm{R}^2+\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^2} \\ \mathrm{Z} & =\sqrt{100^2+100^2} \\ \mathrm{Z} & =100 \sqrt{2} \Omega \\ \mathrm{i}_{\mathrm{rms}} & =\frac{\mathrm{V}_{\mathrm{rms}}}{\mathrm{Z}} \\ \therefore \quad \mathrm{i}_{\mathrm{rms}} & =\frac{200 \sqrt{2}}{100 \sqrt{2}} \\ \mathrm{i}_{\mathrm{rms}} & =2 \mathrm{~A}\end{aligned}$

Asked in: MHT CET 2023 (12 May Shift 1)

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