Give two definitions of mutual inductance, give its units and write factors on which its value depends.
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
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- [IIT 1998]
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