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