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Question 6.38: The current through a 40-mH inductor is i(t)= 0, t0 . Find t...

The current through a 40-mH inductor is

i(t)=\left\{\begin{array}{ll}0, & t<0 \\t e^{-2 t} \mathrm{A}, & t>0\end{array}\right.

Find the voltage v(t).

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\begin{aligned}\mathrm{v}=\mathrm{L} \frac{\mathrm{di}}{\mathrm{dt}} &=40 \times 10^{-3}\left(\mathrm{e}^{-2 \mathrm{t}}-2 \mathrm{te}^{-2 \mathrm{t}}\right) \mathrm{dt} \\&=40(1-2 \mathrm{t}) \mathrm{e}^{-2 t}\mathrm{mV}, \mathrm{t}>0\end{aligned}

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