Give two definitions of mutual inductance, give its units and write factors on which its value depends.

The flux $\Phi_{2}$ linked with the coil-$2$ when current through coil-$1$ is $\mathrm{I}_{1}$ is $\Phi_{2}=\mathrm{M}_{21} \mathrm{I}_{1}$.

Taking $\mathrm{I}_{1}=1$ unit, $\Phi_{2}=\mathrm{M}_{21}$. Thus,

"The magnetic flux linked with one of the coils of a system of two coils per unit current passing through the other coil is called mutual inductance of the system formed by the two coils."

Mutual emf produced in coil-2 is given by,

$\varepsilon_{2}=-\mathrm{M}_{21} \frac{d \mathrm{I}_{1}}{d t}$

When $\frac{d \mathrm{I}_{1}}{d t}=1$ unit in the equation $(2)$,

$\varepsilon_{2}=\mathrm{M}_{21}$. Thus,

"The mutual emf generated in one of the two coils due to a unit rate of change of current in the other coil is called mutual inductance of the system of two coils".

The unit of mutual inductance is

$\mathrm{WbA}^{-1}=\frac{\mathrm{V} \cdot s}{\mathrm{~A}}=$ henry $(\mathrm{H})$

The value of mutual inductance of a system of two coils depends upon :

$(1)$ Shape of coils

$(2)$ Size of coils

$(3)$ Number of turns in two coils

$(4)$ Distance between them

$(5)$ Angle of mutual inclination

$(6)$ The material on which they are wound