A coil of inductance 1.0 H and resistance 100 Omega is connected to a battery of emf 12 V. Find the energy stored in the magnetic field associated with the coil at an instant 10 ms after the circuit is switched on.

Explanation

The energy in the magnetic field associated with the coil is ` U = (1)/(2) Li^2 = (1)/(2) L [(epsilon)/( R) (1-e^(-t/tau)]^2`
The time constant of the circuit is `tau =(L)/(R ) = (1
0H)/(100 Omega) = 10 ms`
Putting the numerical values in (i), the energy at t = 10 ms is `(1)/(2)X(1
0H)X[0
12 A(1-1/e)]^2` = 2
8 mj