Q140 / 180 · COMEDK 2013 · Physics

In an $L-C-R$ circuit, the potential difference between the terminals of the inductance is $60 \mathrm{~V}$, between the terminals of the capacitor is $30 \mathrm{~V}$ and that between the terminals of resistance is $40 \mathrm{~V}$. The supply voltage will be equal to

  • A
    $130 \mathrm{~V}$
  • B
    $10 \mathrm{~V}$
  • Correct answer
    C
    $50 \mathrm{~V}$
  • D
    $70 \mathrm{~V}$

Solution

Given, $V_{R}=40 \mathrm{~V}, V_{L}=60 \mathrm{~V}, V_{C}=30 \mathrm{~V}$ For an $L-C-R$ circuit, the supply voltage $$ \begin{aligned} V &=\sqrt{V_{R}^{2}+\left(V_{L}-V_{C}\right)^{2}} \\ &=\sqrt{40^{2}+(60-30)^{2}} \\ &=\sqrt{40^{2}+30^{2}} \\ &=\sqrt{1600+900}=\sqrt{2500}=50 \mathrm{~V} \end{aligned} $$

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

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