Question

Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon
(A) Relative position and orientation of the two coils
(B) the materials of the wires of the coils
(C) the current in the two coils
(D) the rates at which currents are changing in the two coils

Answer 1

Hint :In order to answer this question we need to understand that when two coils are brought in proximity with each other the magnetic field in one of the coils tends to link with the other. This further leads to the generation of voltage in the second coil. This property of a coil which affects or changes the current and voltage in a secondary coil is called mutual inductance.

Complete Step By Step Answer:
When two coils are brought in the neighbourhood 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 as,
 $ {M_{sp}} = \dfrac{{{N_s}{\phi _s}}}{{{I_p}}} $
 $ {N_s}{\text{ is the number of winding in second coil}} $
 $ {\phi _s}{\text{ is the flux in one turn of second coil due to change in current }}{{\text{I}}_p}. $
The coupled flux of two coils system is used to define the mutual inductance between the coils. The mutual inductance between the coils is,
 $ {M_{21}} = \dfrac{{{N_2}{\phi _{21}}}}{{{I_1}}} $
So, it is defined as the proportionality between the emf generated in coil 2 due to the current flows in coil 1. Thus, it depends on the relative position and orientation of two coils.
So, the correct answer is option (A).

Note :
It should be remembered that mutual inductance between two coils depends on the permeability of the 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. mutual inductance between two coils depends on the number of turns and magnetic flux which further depends on cross section area and permeability.