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NEETPhysicsAlternating Current

A series LCR circuit with inductance 2 H and resistance 10 is connected to an AC source of voltage V = 200 (100t) volt. If the current and voltage in the circuit are in phase, the value of capacitance and the impedance of the circuit are respectively:

Options

  1. A5 mF , 10
  2. B50 F , 200
  3. C50 F , 10
  4. D5 F , 10

Correct answer

C. 50 F , 10

Step-by-step solution

From the given voltage equation V = 200 (100t) , the angular frequency of the source is = 100 rad s ⁻¹ . Since the current and voltage are in phase, the circuit is in resonance. At resonance, the inductive reactance equals the capacitive reactance ( L = 1 C ). C = 1 ^2 L = 1 (100)^2 2 = 1 20000 F C = 50 10⁻⁶ F = 50 F At resonance, the impedance of the circuit is purely resistive and is equal to the resistance R . Z = R = 10 Answer: 50 F , 10

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