Q157 / 180 · COMEDK 2024 (Evening Shift) · Physics

In the A. C. circuit given below, an inductor, capacitor, and resistor ($R = 110\text{ }\Omega$) are in series with a $220\text{ V}, 50\text{ Hz}$ source. Voltmeters $V_1$ (across the inductor) and $V_2$ (across the capacitor) read $100\text{ V}$ each. Find the reading of the voltmeter $V_3$ (across the resistor) and the ammeter A. Figure

  • A
    110 V, 2 A
  • B
    220 V, 1 A
  • Correct answer
    C
    220 V, 2 A
  • D
    110 V, 4 A

Solution

$V_L = V_C = 100$ V, so they cancel (circuit is at resonance).

$V = \sqrt{V_R^2 + (V_L - V_C)^2} = \sqrt{V_R^2 + 0}$

$220 = V_R \Rightarrow V_3 = 220$ V

At resonance, $Z = R = 110\ \Omega$

$I = \dfrac{V_R}{R} = \dfrac{220}{110} = 2$ A

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

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