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(a) The current through two inductors, of self-inductance 12 mH and 30 mH respectively, is increasing with time at the same rate. Draw graphs showing the variation of the (i) emf induced with the rate of change of current in each inductance, (ii) energy stored in each inductor with the current flowing through it. (b) Compare the energy stored in the coils if the power dissipated in the coils is the same. |
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Answer» Solution :(a) (i) Here `L_(1) = 12 mH, L_(2) = 30 mH and (dI_(1))/DT = (dI_(2))/dt = .K.` (say) Then `varepsilon_(1)= - L_(1) (dI_(1))/dt = - kL_(1) and varepsilon_(2) = - L_(2) (dI_(2))/dt = - kL_(2)` Graphs showing variation of induced emf with rate of CHANGE of current in each coil are shown in Fig. 6.53. (ii) ENERGY stored `U = 1/2 LI^(2)` HENCE `U_(1) = 1/2 L_(1)I_(1)^(2) and U_(2) = 1/2 L_(2)I_(2)^(2)` variation of energy stored in each inductor with the current flowing through them are shown in Fig. 6.54. (b) As power is defined as the rate of consumption of energy and power dissipated in the two coils is the same, hence energy of the two coils is also the same. 
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