In the circuit of Fig. 6.82, i_{o}(0) = 2 A. Determine i_{o}(t) and v_{o}(t) for t > 0.
Question 6.60: In the circuit of Fig. 6.82, io(0) = 2 A. Determine io(t) an...
L_{e q}=3 / / 5=\frac{15}{8}
v_{o}=L_{e q} \frac{d i}{d t}=\frac{15}{8} \frac{d}{d t}\left(4 e^{-2 t}\right)=-15 e^{-2 t}
\mathrm{i}_{0}=\frac{\mathrm{I}}{\mathrm{L}} \int_{0}^{\mathrm{t}} \mathrm{v}_{0}(\mathrm{t}) \mathrm{dt}+\mathrm{i}_{0}(0)=2+\frac{1}{5} \int_{0}^{\mathrm{t}}(-15) \mathrm{e}^{-2 \mathrm{t}} \mathrm{dt}=2+\left.1.5 \mathrm{e}^{-2 \mathrm{t}}\right|_{0} ^{\mathrm{t}}={0.5+1.5 \mathrm{e}^{-2 \mathrm{t}} \mathrm{A}}
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