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MHT CET202525 Apr 2025Evening ShiftPhysicsAlternating CurrentActual

An a.c. source of frequency ' f ' is connected to a circuit containing an inductance ' L ' and resistance ' R ' in series. The impedance of this circuit is

Options

  1. AR ^2+2 fL ^2
  2. BR^2+L^2
  3. CR +2 fL
  4. DR^2+4 ^2 f^2 L^2

Correct answer

D. R^2+4 ^2 f^2 L^2

Step-by-step solution

Inductive reactance X_L depends on angular frequency and inductance L , with X_L = L . Given = 2 f , it follows that X_L = 2 f L . In a series RL circuit, the impedance Z is the phasor sum of resistance R and inductive reactance X_L , yielding Z = R^2 + X_L^2 . Substituting for X_L provides Z = R^2 + (2 f L)^2 = R^2 + 4 ^2 f^2 L^2 . The derived expression corresponds to option D .

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