The self induced emf of a coil is 25 volts.

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:

  1. (1) $740 \mathrm{~J}$

  2. (2) $437.5 \mathrm{~J}$

  3. (3) $540 \mathrm{~J}$

  4. (4) $637.5 \mathrm{~J}$


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,

$\Delta \mathrm{E}=\frac{1}{2} \mathrm{~L}\left(\mathrm{i}_{1}^{2}-\mathrm{i}_{2}^{2}\right)=\frac{1}{2} \times \frac{5}{3} \times\left(25^{2}-10^{2}\right)$

$=\frac{5}{6} \times 525=437.5 \mathrm{~J}$

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