The current through two inductors of self inductance 12 mH and 30 mH is increasing with time at the same rate. Draw graphs showing the variation of the (a ) e.m.f. induced with the rate of change of current in each inductor. (b) enargy stored in each inductor with the current flowing through it.
Compare the energy stored in the coils if power dissipated in the coil is same.

Explanation

(b) As `E_(1) = L_(1) (dI)/(dt)`
& `E_(1)I = L_(1) Id//dt`
`dw_(1) = E_(1)I dt = L_(1) IdI_(1)`, Integrating
`w_(1) = (1)/(2) L_(1)I^(2)`
Similarly, `w_(2) = (1)/(2) L_(2) I^(2)`
As the circuits are purely ideal i.e., ohmic resistances are zero.
`:.` Power consumed by the two circuits is zero.