Question:
The self induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from $10 \mathrm{~A}$ to $25 \mathrm{~A}$ in $1 \mathrm{~s}$, the change in the energy of the inductance is:
Correct Option: , 2
Solution:
(2) According to faraday's law of electromagnetic induc-
tion, $\mathrm{e}=\frac{-\mathrm{d} \phi}{\mathrm{dt}}$
$\mathrm{L} \times \frac{\mathrm{di}}{\mathrm{dt}}=25 \Rightarrow \mathrm{L} \times \frac{15}{1}=25$
or, $\mathrm{L}=\frac{5}{3} \mathrm{H}$
Change in the energy of the inductance,
$\Delta \mathrm{E}=\frac{1}{2} \mathrm{~L}\left(\mathrm{i}_{1}^{2}-\mathrm{i}_{2}^{2}\right)=\frac{1}{2} \times \frac{5}{3} \times\left(25^{2}-10^{2}\right)$
$=\frac{5}{6} \times 525=437.5 \mathrm{~J}$