When a current i = 10 sin `(100 pi t)` A is passed through a coil, an induced emf having a maximum value of `5 pi V` is produced in a nearby coil kept parallel to the first coil. What is the mutual inductance between the two coils?

Options

A. 20 mH
B. 15 mH
C. 10 mH
D. 5 mH

Answer

D

Explanation

`i=10 sin (100 pi t)`
`:. (dI)/(dt) = 10 xx 100 pi cos (100 pi t)`
Maximum `((dI)/(dt)) = 10 xx 100 pi = 1000 pi`
`e_(max) = M((dI)/(dt))_(max) ("numerically")
`:. 5 pi = M (1000 pi)`
`:. M = 5/1000 = 5 xx 10^(-3)H = 5 mH`.