Question

Two (insulated) coils are wound, (one over the other), on a solenoid core. If the number of turns, per unit length, of the first coil and of the second coil, were to be increased by a factors of 3 and 4, respectively, the self inductance of the two coils (L₁ and L₂) and their mutual inductance (M), would increase (respectively) by factors of

(1) 3, 4 and 12

(2) 3, 4 and 4/3

(3) 9, 16 and 16/9

(4) 9, 16 and 12

Answer 1

(4) 9, 16 and 12

We know that the self inductance, of a solenoidal coil, is proportional to n² (n = number of turns per unit length). 

Hence the self inductances, of the two coils will increase by factors of 3² and 4² , i.e. 9 and 16.

The mutual inductance of the two solenoid coils (one over the other) is proportional to the product n₁ n₂ (n₁ , n₂ are the number of turns per unit length in the two coils). 

Hence M, in the given case, would increase by a factor of 3 x 4, i.e. (12).