Q152 / 160 · TS EAMCET 2024 (10 May Shift 2) · Physics

An inductor of inductive reactance $R$, a capacitor of capacitive reactance $2 R$ and a resistor of resistance $R$ are connected in series to an ac source. The power factor of the series LCR circuit is

  • Correct answer
    A
    $\frac{1}{\sqrt{2}}$
  • B
    $\frac{1}{\sqrt{3}}$
  • C
    $\frac{1}{4}$
  • D
    $\frac{\sqrt{3}}{2}$

Solution

For LCR series circuit, $\begin{aligned} & \mathrm{X}_{\mathrm{L}}=\mathrm{R}, \mathrm{X}_{\mathrm{C}}=2 \mathrm{R} \\ & \therefore \mathrm{z}=\sqrt{\mathrm{R}^2+\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^2}=\sqrt{\mathrm{R}^2+(\mathrm{R}-2 \mathrm{R})^2}=\sqrt{2 \mathrm{R}} \\ & \therefore \text { Power factor, } \cos \phi=\frac{\mathrm{R}}{\mathrm{Z}}=\frac{\mathrm{R}}{\sqrt{2} \mathrm{R}}=\frac{1}{\sqrt{2}}\end{aligned}$

Hence, the correct answer is option: 'A'.

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