The voltage across a 200-mH inductor is given by
v(t) = 3t^{2} + 2t + 4 V for t > 0.
Determine the current i(t) through the inductor. Assume that i(0) = 1 A.
Question 6.39: The voltage across a 200-mH inductor is given by v(t) = 3t^2...
\mathrm{v}=\mathrm{L} \frac{\mathrm{di}}{\mathrm{dt}} \longrightarrow \mathrm{i}=\frac{1}{\mathrm{L}} \int_{0}^{\mathrm{t}} \mathrm{idt}+\mathrm{i}(0)
\mathrm{i}=\frac{1}{200 \times 10^{-3}} \int_{0}^{\mathrm{t}}\left(3 \mathrm{t}^{2}+2 \mathrm{t}+4\right) \mathrm{dt}+1
=\left.5\left(\mathrm{t}^{3}+\mathrm{t}^{2}+4 \mathrm{t}\right)\right|_{0} ^{\mathrm{t}}+1
\mathrm{i}(\mathrm{t})={5 \mathrm{t}}^{3}+5 \mathrm{t}^{2}+20 \mathrm{t}+1 \mathrm{A}
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