Question

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

Answer 1

According to faraday’s law of electromagnetic induction
$e =\frac{-d\phi}{dt}$
$L\times \frac{di}{dt} = 25$
$\Rightarrow L \times \frac{15}{1} =25$
or, $L = \frac{5}{3}H$
Change in the energy of the inductance,
$\Delta E = \frac{1}{2}L \left(i^{2}_{1} -i^{2}_{2}\right) = \frac{1}{2} \times\frac{5}{3}\times\left(25^{2} -10^{2}\right)$
$= \frac{5}{6}\times525 = 437.5J$