Q192 / 200 · MHT CET - Medical 2026 (26 April Shift 1) · Physics

A series LCR circuit is connected to a source of alternating e.m.f. of $50$ V. The potential difference across inductor and capacitor is $80$ V and $50$ V respectively. The potential difference across the resistor is

  • A
    $80$ V
  • B
    $70$ V
  • C
    $50$ V
  • Correct answer
    D
    $40$ V

Solution

In a series LCR circuit, the relationship between the applied voltage $V$ and the voltages across the resistor $V_R$, inductor $V_L$, and capacitor $V_C$ is given by:

$V = \sqrt{V_R^2 + (V_L - V_C)^2}$

Given:
$V = 50$ V
$V_L = 80$ V
$V_C = 50$ V

Substituting the values into the formula:

$50 = \sqrt{V_R^2 + (80 - 50)^2}$

$50^2 = V_R^2 + 30^2$

$2500 = V_R^2 + 900$

$V_R^2 = 2500 - 900 = 1600$

$V_R = 40$ V

Answer: $40$ V

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

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