Question

The self induced emf of a coil is $25\text{V}$. When the current in it is changed at uniform rate from $10\text{A to}25\text{A}$ in $1\text{s}$, the change in the energy of the inductance is

• A. $740\text{J}$
• B. $437.5\text{J}$
• C. $540\text{J}$
• D. $637.5\text{J}$

Answer 1

The correct option is B $437.5\text{J}$

According to faraday's law of electromagnetic induction,
$e=\frac{-d\Phi }{dt}$
$L\times \frac{di}{dt}=25\Rightarrow L\times \frac{15}{1}=25$
$L=\frac{5}{3}\text{H}$

Change in the energy of the inductance,
$\Delta E=\frac{1}{2}L(i_1^2-i_2^2)=\frac{1}{2}\times \frac{5}{3}\times ({25}^2-{10}^2)$
$\Delta E=\frac{5}{6}\times 525=437.5\text{J}$.