My Thinking

Inductors Connected in Series Current remains same in both the coils. The induced emf in both coils is given below Let e be the induced emf of  equivalent inductor of  equivalent inductance L. Inductors Connected in Parallel In parallel combination current distributes its self Differentiates both sides with respect to time.  ---equation 1 Since both coils are connected in parallel so  potential remains same .    ---equation 2  ---equation 3  ---equation 4 Substitute values from equation 2,3,4 in equation 1 Visit PHYSICS page for more blogs  

In above figure we have two concentric coplanar coils (Primary coil of radius R and Secondary coil of radius r).Due to flux change in primary coil there will be a induced emf in secondary coil. Magnetic field due to primary coil is  flux change in secondary coil depends on current in primary coil Mutual Inductance is shown below   Visit PHYSICS page for more blogs

As we have variable source with increasing current in primary coil ,there will be a flux change in primary coil. Due to this flux change in primary coil there will be a flux change in secondary coil and this flux change in secondary coil will generate induced emf in secondary coil. This is called mutual induction. flux linked with secondary coil depends on current in primary coil ,so they are directly proportional to each other. differentiate with respect to time both sides   ------equation 1 As per faraday law induced emf in secondary coil is  ------equation 2 substitute value from equation 1 to equation 2   Visit PHYSICS page for more blogs

As shown in figure we have a long solenoid of length l and current i .Magnetic field for long solenoid is given below. where n is number of turns per unit length and N is total number of turns. As we know that magnetic flux linked with the coil is proportional to the current in coil.    Hence Self inductance of long solenoid is given below Visit PHYSICS page for more blogs

As shown in figure we have a current carrying coil whose radius is r and Magnetic field at the center of the coil due to its own current is given below. As we know that magnetic flux linked with the coil is proportional to the current in coil.    Visit PHYSICS page for more blogs

As the current is increasing in our circuit so there will be a induced emf and induced current in the coil which will oppose this increasing current. So work should be done against this induced (emf and current) to maintain current i from battery source. divide by dt both sides remove dt from both sides integrating both sides (work done increases from 0 to w and current increases from 0 to i) so total energy supplied when current increases from zero to final value. Visit PHYSICS page for more blogs