Module 3 : MAGNETIC FIELD
Lecture 19 : Mutual Inductance
Self Inductance :
  Even when there is a single circuit carrying a current, the magnetic field of the circuit links with the circuit itself. If the current happens to be time varying, an emf will be generated in the circuit to oppose the change in the flux linked with the circuit. The opposing voltage acts like a second voltage source connected to the circuit. This implies that the primary source in the circuit has to do additional work to overcome this back emf to establish the same current. The induced current has a direction determined by Lenz's law.
If no ferromagnetic materials are present, the flux is proportional to the current. If the circuit contains $N$turns, Faraday's law gives
 
\begin{displaymath}N\frac{d\Phi}{dt} = -L\frac{dI}{dt}\end{displaymath}
  where $L$is known as Self Inductance of the circuit. By definition, $L$is a positive quantity. From the above it follows, on integrating,
 
\begin{displaymath}N\Phi = LI +\ \ {\rm constant}\end{displaymath}
  Since $\Phi=0$when $I=0$, the constant is zero and we get
 
\begin{displaymath}L = \frac{N\Phi}{I}\end{displaymath}
  The self inductance can, therefore, interpreted as the amount of flux linked with the circuit for unit current. The emf is given by
 
\begin{displaymath}{\cal E} = -N\frac{d\Phi}{dt}= -L\frac{dI}{dt}\end{displaymath}
  Example-24
   
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