1 ) When current in a coil changes to 8 ampere from 2 ampere in 3 x 10 ^ ( -3 ) sec , then emf induced in the coil is 2 volts . The self inductance of coil is ?

1 )  When current in a coil changes to 8 ampere from 2 ampere in 3 x 10 ^ ( -3 ) sec , then emf induced in the coil is 2 volts . The self inductance of coil is . . . . . . . . . ?

A ) 10 ^ ( +3 )  Henry  ,                    B ) 10 ^ ( -3 )  Henry  ,

C ) 10 ^ ( -6 )  Henry  ,                     D ) 10 ^ ( -9 )  Henry  ,

Correct Answer : -    B ) 10 ^ ( -3 )  Henry  ,

Solution : -

Formula : -

We have formula  that : -

E = d ( NΦ ) / dt   =   d ( LI ) / dt    =   L . dI / dt  ,

Ø    E   =   L . dI /dt  , 

Ø     2  =  ( L x 6 ) / 3 x 10 ^ ( -3 )    ,

Ø    L = 10 ^ ( -3 )    Henry  ,   Answer .

 

2 ) If in a coil rate of change of area is 15  m² / millisecond and current become 1 amp from 2 amp in  2 x 10 ^ ( -3 ) sec magnitude of field 1 Tesla , then self inductance of coil is . . . . . . . ?

A ) 7 Henry  ,                                           B ) 10 Henry  ,

C ) 13 Henry  ,                                         D ) None of these ,

Correct Answer : -   B ) 10 Henry  ,

Solution : -

So we have formula : -

N Φ = LI  ,  so we  take derivative  : -

Ø   N ( dΦ / dt )  =  L . ( dI / dt )  ,   ………… eq.1

So  Φ = B.A ,

dΦ / dt  =  1 . ( dA / dt )  ,     since ( B = 1 )  .

So put in eq .1 : -

Ø   N.1.( dA / dt )  =  L ( dI / dt )  ,    so put values ;

Ø    (1 x 1 x 5) / 10^(-3)   =  (L x 1) / 2 x 10^(-3)    ,

Ø    L = 10 Henry  ,   Answer .