Question

The self induced emf of a coil is $25$ volts. When the current in it is changed at uniform rate from $10A$ to $25A$ in $1s$, the change in the energy (in joule) of the inductance is:

Answer 1

Answer: 437.5

According to faraday’s law of electromagnetic induction
$e=\frac{-d\varphi }{dt}$
$L\times \frac{di}{dt}=25$
$\Rightarrow L\times \frac{15}{1}=25$
or, $L=\frac{5}{3}H$
Change in the energy of the inductance,
$\Delta E=\frac{1}{2}L\left(i_1^2-i_2^2\right)=\frac{1}{2}\times \frac{5}{3}\times \left(25^2-10^2\right)$
$=\frac{5}{6}\times 525=437.5J$