Question

Give the expression for energy stored in an inductance coil carrying current.

Answer 1

The current flowing through the inductor at any instant is given by $i=i_o{e}^{-Rt/L}$

where $L$ is the inductance of the coil and $R$ is the resistance.

Energy stored in the inductor $E={\int }_o^{\infty }{i}^{2}Rdt$

Or $E={\int }_o^{\infty }{i}_o^2{e}^{-2Rt/L}Rdt$

Or $E=i_o^{2}R{\int }_o^{\infty }{e}^{-2Rt/L}dt$

Or $E=i_o^{2}R\times \frac{e^{-2Rt/L}}{-2R/L}{|}_o^{\infty }$

Or $E=i_o^{2}R\times \frac{(0-1)}{-2R/L}$

$⟹$ $E=\frac{1}{2}{i}_o^{2}L$