Question
What is the self-inductance of a coil which produces $$5\,V$$ when the current changes from $$3\,A$$ to $$2\,A$$ in one millisecond ?
A.
$$5000\,H$$
B.
$$5\,mH$$
C.
$$50\,H$$
D.
$$5\,H$$
Answer :
$$5\,mH$$
Solution :
Emf induced in the coil is given by $$e = - \frac{{d\phi }}{{dt}}$$
If coil has self-inductance $$\left( L \right)$$ and current $$i,$$ then induced emf is given by
$$\eqalign{
& e = - \frac{d}{{dt}}\left( {Li} \right)\,\,{\text{or}}\,\,e = - L\frac{{di}}{{dt}} \cr
& \therefore L = \frac{{\left| e \right|}}{{\frac{{di}}{{dt}}}} \cr} $$
$$\eqalign{
& {\text{Given,}}\,\,\left| e \right| = 5\,V,di = 3 - 2 = 1\,A \cr
& dt = 1\,ms = 1 \times {10^{ - 3}}s \cr
& \therefore L = \frac{{5 \times {{10}^{ - 3}}}}{1} = 5\,mH \cr} $$