Question

A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil?

Answer 1

Mutual inductance of a pair of coils, $\mu$ = 1.5 H
Initial current, $I_1$ = 0 A
Final current $I_2$= 20 A
Change in current, $dI$= $I_1-I_2$ = 20-0 = 20A
Time taken for the change, t = 0.5 s
Induced emf, e=$\frac{d\phi}{dt}$ ...(1)
Where $d\phi$ is the change in the flux linkage with the coil.
Emf is related with mutual inductance as:
e= $\mu\frac{d\phi}{dt}$ ...(2)
Equating equations (1) and (2), we get
$\frac{d\phi}{dt}$ =$\mu\frac{d\phi}{dt}$
$d\phi$ = 1.5 x (20)
=30Wb
Hence, the change in the flux linkage is 30 Wb