In the given figure, an inductor and resistor are connected in series with a battery of emf E volt. E a 2 b J s - 1 represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of b a will be _____.

Step-by-step solution

The formula to calculate the current flowing through an L-R circuit is given by i = E R 1 - e - R t L       . . . 1 The energy stored within the inductor can be calculated as follows: E induction  = 1 2 L i 2 = 1 2 L E 2 R 2 1 - e - R t L 2       . . . 2 The rate of change of energy stored within the inductor is given by d d t E induction  = 2 1 - e - R t L · e - R t L · R L · E 2 L 2 R 2 = E 2 R e - R t L - e - 2 R t L       . . . 3 For maximum