Derivation for Energy Stored in an INDUCTOR

Detailed Answer given by Aishwayra khana is correct.

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  • When an inductor L has a current I flowing through it, the inductor has a magnetic field that stores energy.

  • As the current increases, energy is stored in the magnetic field of the inductor as the field builds up. When the current decreases the stored energy of the magnetic field is released thereby adding to the current.
  • Unlike current flowing through a resistor, energy is not dissipated in an inductor but only stored. Current flow in a resistor is an irreversible process whereas current flow through an inductor is a reversible process.

Mathematical derivation:

The rate at which energy is absorbed or released by inductor can be determined from the ordinary power formula.

Here V is the voltage drop across the inductor.

The energy stored U can be found by integration when the current increases from zero to some value I.

For a DC RL circuit, the expression U = 1/2 L I2 gives be energy stored in the inductor after the circuit is switched on and reaches its steady state value of the current I. If the current is varying with time I(t), then U is still the energy stored in the inductor's Magnetic field at that moment.

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