Question

In circular coil, when number of turns is doubled and resistance becomes 1/4th of initial value, the inductance becomes

Answer 1

When the number of turns is doubled, the inductance becomes 4 times.

Explanation :

Since the inductance is directly proportional to square of the number of turns,

L ∝ N²

when the number of turns doubles,

L₂/L₁ = (N₂/N₁)²

=> L₂/L₁ = 2² = 4

=> L₂ =4L₁

Hence when the number of turns is doubled, the inductance becomes 4 times.

I hope this answer helps you, please feel free to ask any doubts in the comment section.

Answer 2

The self inductance is mainly depends on the geometric equation for number of posts in terms of unit length. The cross sectional areas for themselves inductance of the coil will be directly proportional to increase L and N with vice-versa .

L ∝ N² where N = number of turns, L = inductance.

L₂/L₁ = (N₂/N₁)²

L₂/L₁ = 2² = 4

L₂ =4L₁  

Hence the number of turns for the inductance becomes 4 times.