Question

By a change of current from $5A$ to $10A$ in $0.1s$, the self induced emf is $10V$. The change in the energy of the magnetic field of a coil will be

• A. $5J$
• B. $6J$
• C. $7.5J$
• D. $9J$

Answer 1

Answer: (C)

$\left|\epsilon \right|=L\frac{\Delta I}{\Delta t}$
$L=\frac{|\epsilon |\Delta t}{\Delta I}=\frac{10\times 0.1}{\left(10-5\right)}=0.2H$
The magnetic field energies for currents $I_1$ and $I_2$ are
$U_1=\frac{1}{2}L{I}_1^2$ and $U_2=\frac{1}{2}L{I}_2^2$
Change in energy $=U_2-U_1$
$=\frac{1}{2}L{I}_2^2-\frac{1}{2}L{I}_2^2=\frac{L}{2}\left(I_2^2-I_1^2\right)$
$=\frac{0.2}{2}\left(10^2-5^2\right)$
$=7.5J$