Question

On what factors, mutual inductance between two coils depends?
A. permeability of core
B. the number of their turns
C. cross sectional area of the common core
D. all of above

Answer 1

Hint: A changing current in a coil induced magnetic flux through a neighboring coil. As a result, an emf is induced in neighboring coils. This interaction of one coil’s magnetic field on another coil is known as mutual inductance.

Complete step by step answer:
When two coils are brought in the neighborhood with each other, the magnetic field in one of the coils gets linked with the other coil. This results in the induction of voltage in the second coil. This property of a coil which affects or changes the current and voltage in a secondary coil kept in its proximity is called mutual inductance.
The expression for mutual inductance of second coil with respect to first is given by the expression
${{M}_{sp}}=\dfrac{{{N}_{s}}{{\phi }_{s}}}{{{I}_{p}}}$
Where ${{N}_{s}}$ is the number of windings in second coil, ${{\phi }_{s}}$ is the flux in one turn of second coil due to change in current ${{I}_{p}}$.

Magnetic flux $\phi$ is the measurement of magnetic field passing normally through an area. Magnetic flux through an area is given by dot product of magnetic field and area vector.
$\phi =\mathbf{B}.\mathbf{A}$
We observe that mutual inductance between two coils depends on the number of turns and magnetic flux which further depends on cross section area and permeability.
Therefore, it can be concluded that mutual inductance depends on permeability of core, the number of their turns, cross sectional area of the common core.

So, the correct answer is “Option d”.

Note: Mutual inductance between two coils depends on permeability of core, the number of their turns and cross sectional area of the common core.
Mutual inductance of the coils also depends on their separation as well as their relative orientation.