Q153 / 180 · KCET 2020 · Physics

In the given circuit the peak voltage across $C$, $L$ and $R$ are $30 \mathrm{~V}, 110 \mathrm{~V}$ and $60 \mathrm{~V}$, respectively. The rms value of the applied voltage is
Figure

  • A
    $100 \mathrm{~V}$
  • B
    $200 \mathrm{~V}$
  • Correct answer
    C
    $70.7 \mathrm{~V}$
  • D
    $141 \mathrm{~V}$

Solution

Given, $V_{C}=30 \mathrm{~V}, V_{L}=110 \mathrm{~V}$ and $V_{R}=60 \mathrm{~V}$ The peak voltage across series $L-C-R$ circuit is given by $\begin{aligned} V_{O} &=\sqrt{V_{R}^{2}+\left(V_{L}-V_{C}\right)^{2}} \\ &=\sqrt{(60)^{2}+(110-30)^{2}} \\ &=\sqrt{(60)^{2}+(80)^{2}}=100 \mathrm{~V} \end{aligned}$ $\therefore$ Rms value of voltage, $V_{\text {rms }}=$

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

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