Q169 / 180 · COMEDK 2019 · Physics

In a $L-C-R$ circuit the potential diffcrcnce 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

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

Solution

The $L-C-R$ circuit in series combination and phasor diagram is given below According to the question, Potential difference across resistor, $V_{R}=40 \mathrm{~V}$ Potential difference across inductor, $V_{L}=60 \mathrm{~V}$ Potential difference across capacitor, $V_{C}=30 \mathrm{~V}$ Magnitude of potential difference supplied is given by $$ \begin{aligned} V &=\sqrt{V_{R}^{2}+\left(V_{L}-V_{C}\right)^{2}}=\sqrt{40^{2}+(60-30)^{2}} \\ &=\sqrt{(40)^{2}+(30)^{2}}=\sqrt{2500} \\ &=50 \mathrm{~V} \end{aligned} $$

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

Relevant Questions