Question

A coil of inductance $2\text{H}$ having negligible resistance is connected to a source of supply whose voltage is given by $V=3t\text{V}$, where $t$ is time in $\text{s}$. If the voltage is applied when $t=0$, then the energy stored in the coil after $4\text{s}$ is _______$\text{J}$.

Answer 1

We know that,
$V=L\frac{di}{dt}$
$\Rightarrow 3t=L\frac{di}{dt}$

$\Rightarrow L{\int }_0^{i}di=3{\int }_0^{t}tdt$

$\Rightarrow Li=\frac{3t^2}{2}$

$\Rightarrow i=\frac{3t^2}{2L}=\frac{3\times 4^2}{2\times 2}=12\text{A}$

Now, energy stored in the coil,
$E=\frac{1}{2}L{i}^2=\frac{1}{2}\times 2\times {12}^2=144\text{J}$