Self Inductance - Practice Questions & MCQ

Inductance-

It is the property of electrical circuits that oppose any change in the current in the circuits.

Inductance is analogous to inertia in mechanics.

Self Inductance-

Whenever the electric current passing through a coil or circuit changes, the magnetic flux linked with it will also change. And to oppose this flux change according to Faraday’s laws of electromagnetic induction, an emf is induced in the coil or the circuit. This
phenomenon is called ‘self-induction’.

or Self-inductance is defined as the induction of a voltage in a current-carrying wire when the current in the wire itself is changing.

And the emf induced is called back emf, current so produced in the coil is called induced current.

And the direction of induced current for case A and case B  is shown below.

Coefficient of self induction (L)-

If $\phi$ is the flux linkages associated with 1 turn of the coil. And if N is the number of turns in the coil.

Then total flux linkage associated with the coil is $N \phi$
And this total flux linkage is directly proportional to the current in the coil. l.e $N \phi \alpha i$
or we can write $\phi_{\text {total }}=\phi_T=N \phi=L i$
where $L=$ coefficient of self-induction.
So the coefficient of self-induction is given as $L=\frac{N \phi}{I}$
- If $i=1 \mathrm{amp}, N=1$ then, $L=\phi$

      i.e  The coefficient of self-induction of a coil is equal to the flux linked with the coil when the current in it is 1 amp.

Faraday Second Law of Induction emf-    

Using $\phi_{\text {total }}=N \phi=L i \quad$ and $\varepsilon=\frac{-d \phi_T}{d t}$
we get

$
\varepsilon==-N \frac{d \phi}{d t}=-L \frac{d i}{d t}
$
If $\frac{d i}{d t}=1 \frac{a m p}{s e c}$ and $N=1$ then $|\varepsilon|=L$
i.e The coefficient of self-induction is equal to the emf induced in the coil when the rate of change of current in the coil is unity.

Units and dimensional formula of ' $L$ '-
S.I. Unit - Henry (H)

And

$
1 H=\frac{1 V \cdot \sec }{A m p}
$

And its dimensional formula is $M L^2 T^{-2} A^{-2}$

Dependence of self-inductance (L)-

It depends upon the number of turns $(\mathrm{N})$, Area $(\mathrm{A})$ and permeability of medium $(\mu)$. 'L' does not depend upon current flowing or change in current flowing.