Question

Two inductances $L_1$ and $L_2$ are connected in series and are separated by a large distance:
(i) Show that their equivalent inductance is $L_1+L_2$.
(ii) Why must their separation be large?

Answer 1

( i )

To prove that equivalent inductance [in series] is $L_1$ and $L_2$

Let a common current $I$ be flowing, in the circuit, passing through $L_1$ and $L_2$.

i.e. $I=I_{L_1}+I_{L_2}$ ($1$)

According to Kirchhoff's Voltage Law,

$V=V_{L_1}+V_{L_2}$ ($2$)

Also, we know that

$V=L\frac{di}{dt}$

Putting in equation ($2$)

$L\frac{di}{dt}=L_1\frac{di}{dt}+L_2\frac{di}{dt}$ ($3$) [since, $I$ is same across $AB$]

Dividing the above equation by $\frac{di}{dt}$ both sides

$L=L_1+L_2$.

( ii )
When two or more coils are magnetically linked together by a common magnetic flux, they are said to have a property of mutual induction. This mutual inductance can be a negative thing, as leakage inductance from coil can interfere with the operation of other adjacent components.

Thus the separation should be large.