Question

The mutual inductance of a pair of coils placed close to each other depends upon

• A. The rate at which currents are changing in the two coils.
• B. Relative position and orientation of the two coils
• C. The materials of the wires of the coils
• D. The current in the two coils

Hint:

\(M=\phi_2/I_1\) is a geometric quantity.

Answer 1

The Correct Option is B

Step 1: Understanding the concept.
Mutual inductance M links the emf in one coil to the changing current in the other, through \(\varepsilon = -M\frac{dI}{dt}\). It is a geometric property of the pair.

Step 2: Check option (1).
The rate of change of current sets the emf, not M itself. M is the same whatever the rate. So option 1 is wrong.

Step 3: Check option (2).
M depends on how much flux of one coil links the other. That depends on the distance, the number of turns, the area, the medium and the relative orientation of the coils. So option 2 is right.

Step 4: Check option (3).
The wire material only changes resistance, not the flux linkage. So option 3 is wrong.

Step 5: Check option (4).
M is defined per unit current, so it does not depend on the current value. Option 4 is wrong.

Final Answer:
Mutual inductance depends on the relative position and orientation of the coils. \[ \boxed{\text{Option 2}} \]