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JEE MainPhysicsElectromagnetic Induction

An inductor of inductance 5 H and a resistor of resistance 8 , are connected in series to a DC battery of EMF 24 V. After the circuit is closed, the maximum rate at which energy is being stored in the magnetic field of the inductor during the growth of current is

Options

  1. A18 W
  2. B36 W
  3. C72 W
  4. D9 W

Correct answer

A. 18 W

Step-by-step solution

The rate at which energy is stored in the magnetic field of the inductor is the instantaneous power delivered to it, given by: P_L = V_L i From Kirchhoff's voltage law, the voltage across the inductor is V_L = E - iR . Substituting this into the power equation: P_L = (E - iR)i = Ei - i^2 R To find the maximum rate of energy storage, we differentiate P_L with respect to i and set it to zero: dP_L di = E - 2iR = 0 i = E 2R Substituting the given values E = 24 V and R = 8 , : i = 24 2 8 = 1.5 A The maximum rate of ene

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