My Thinking

In above figure when current passing through the circuit and coil changes (increasing in our case) the magnetic flux linked with the coil also changes ,due to which an EMF will be induced in the coil(this phenomenon is called self induction) .This induced EMF and induced current will be in opposite direction(as current is increasing in our case) . As the flux linked with the coil increases as current increases, hence flux linked with coil is directly proportional to current.                                                                 remove proportionality sign and put constant L Differentiate both sides wrt time     -----equation 1 By Faraday's Law , Induced EMF is given by below equation -----equation 2 Substitute value from equation 1 to equation 2   Visit PHYSICS page for more blogs

Now Suppose from  LR Circuit (Growth of Current)  when current in our circuit reaches we change the switch position from A to B , So after changing switch the current in circuit starts decaying and energy stored in inductor will convert to thermal energy. Integrating both sides (Current changes from  to i ) The Current time graph for above equation is shown below .Here the current reduces with time.   Visit PHYSICS page for more blogs

Here in above circuit we have inductor (L) ,resistor(R) and DC source(V). When we are going to close the switch S the current in the circuit will start increasing and due to this an EMF  will be induced in the inductor. This induced EMF will oppose the current i in the circuit.  integrating both sides(Current rises from 0 to i and time from 0 to t) Current time Graph for above equation is shown below.   Visit PHYSICS page for more blogs