Question

Choose the correct option/options

• A. Two coils having self inductances $L_1$ and $L_2$ can have maximum mutual inductance $\sqrt{L_1{L}_2}$.
• B. Closer two circular coils parallel to each other and centres along a common axis are placed less is the coupling constant.
• C. Coupling constant has value between $0$ and $1$.
• D. The coupling constant depends on the geometry of the coils.

Answer 1

Answer: (A), (C), (D)

The coupling constant depends on the geometry of the coils.

The coefficient of coupling can be defined as the fraction of the magnetic flux produced by the current in one coil that links with the other coil.

It is represented by the symbol $\left(K\right)$ and the amount of coupling between two inductively coupled coils is expressed in terms of the coefficient of coupling.

It can be given as:

$K=\frac{M}{\sqrt{L_1{L}_2}}$

Where,

$M=$ mutual inductance between two coils
$L_1$ = self inductance of the first coil
$L_2$ = self-inductance of the second coil

The value of coupling constant always lies between $0$ and $1$.

When two coils are wound in such a way that flux linked with one coil is perfectly linked to the other coil, then the value of $K$ is $1$.

In that case $M=\sqrt{L_1{L}_2}$

This is the maximum value of mutual inductance between two coils.

Also, the closer the coils are, the more is the coupling constant.

Hence, options $\left(A\right)$, $\left(C\right)$ and $\left(D\right)$ are correct.