Question

An inductor stores u energy and I current is passed through it and dissipate energy at the rate of P.The time constant of the circuit,when this coil is connected across a battery of zero internal resistance?

Answer is 2U/p

Answer 1

Energy stored in an inductor `L` is given by

`U=1/2LI^2`
where `I` is final value of the current.

Power dissipated `P` in a resistor `R` is given as

`P=I^2R`

Time constant of `LR` circuit is given as

`tau = L/R`

Writing it in terms of `Land R`, and noting that internal resistance of the battery is zero, we get

`tau=((2U)/I^2)/(P/I^2)`
`tau=(2U)/(P)`