Question

Two current-carrying coils have radii r and 4r and have same magnetic induction at their centres. The ratio of voltage applied across them is ______.

Options

• 1: 4

• 8: 1

• 4: I

• 1: 8

Answer 1

Two current-carrying coils have radii r and 4r and have same magnetic induction at their centres. The ratio of voltage applied across them is 4: 1. 

Explanation:

For the given two coils, magnetic induction at their centres is the same.

Let `"B"_1 = "B"_2`

`("µ"_0"I"_1)/(2"r") = ("µ"_0"I"_2)/(2(4"r"))`

`=> "I"_1/ "I"_2 = 1/4`

Using Ohm's Law,

`"V" alpha 1/"I"`

∴ `"V"_1/"V"_2 = 1/4`