Two different coils have self indutance 8 mH and 2 mH. The current in both coils are increased at same constant rate. The ratio of the induced emf's in the coil is

Options

A. ` 4: 1 `
B. ` 1 : 4 `
C. ` 1 : 2 `
D. `2 : 1 `

Answer

A

Explanation

The induced emf , ` e = ( Ldi ) /( dt ) `
Here, ` L _ 1 = 8 m H = 8 xx 10 ^( - 3 ) H `
and ` L _ 2 = 2 m H = 2 xx 10 ^( -3 ) ` H
So, ratio of inducedd emf's ` ( e _ 1 ) /( e_ 2 ) = ( L _1 (di )/( dt ) ) /( L _ 2 ( di )/( dt)) = ( L _ 1 )/( L _ 2 ) `
( Since, current is increased at same rate )
` rArr ( e _ 1 ) / ( e_ 2 ) = ( 8 xx 10 ^( -3 ) H )/( 2 xx 10 ^( -3 ) H ) = ( 4 )/ (1 ) `