Q85 / 100 · BITSAT 2022 · Physics

In the circuit shown in the figure, the $\mathrm{AC}$ source gives a voltage $V=20 \cos (2000 t)$ neglecting source resistance, the voltmeter and ammeter reading will be Figure

  • A
    $0 \mathrm{~V}, 0.47 \mathrm{~A}$
  • Correct answer
    B
    $282 \mathrm{~V}, 1.41 \mathrm{~A}$
  • C
    $1.41 \mathrm{~V}, 0.47 \mathrm{~A}$
  • D
    $15 \mathrm{~V}, 837 \mathrm{~A}$

Solution

Given, $R_1=8 \Omega$ $\begin{aligned} R_2 & =2 \Omega \\ L & =5 \mathrm{mH} \\ C & =50 \mu \mathrm{F}\end{aligned}$ and $\quad V_0=20 \cos (2000 t)$ Impedance, $Z=\sqrt{R^2+\left(X_L-X_C\right)^2}$ As, here, $X_L=\omega L=2000 \times 5 \times 10^{-3}=10 \Omega$ Similarly, $X_L=\frac{1}{\omega C}=\frac{1}{2000 \times 50 \times 10^{-6}}=10 \Omega$ $\because \quad X_L=X_C$, Hence, $i_{\max }=\frac{V_0}{Z}=\frac{20}{(8+2)}=2 \mathrm{~A}$ Hence, $\quad i_{\operatorname{rms}}=\frac{i_{\max }}{\sqrt{2}}=\frac{2}{\sqrt{2}}=1.41 \mathrm{~A}$ and $$ \begin{aligned} V & =R_2 i_{\mathrm{rms}}=1.41 \times 2 \\ & =282 \mathrm{~V} \end{aligned} $$

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

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