Consider the circuit in Fig. 6.83. Find: (a) L_{eq}, i_{1}(t) and i_{2}(t) if i_{s}=3e^{-t} mA , (b) v_{o}(t), (c) energy stored in the 20-mH inductor at t=1s.
Question 6.61: Consider the circuit in Fig. 6.83. Find: (a) Leq, i1(t) and ...
(a) L_{e q}=20 / /(4+6)=20 \times 10 / 30=6.667 \mathrm{mH}
Using current division,
i_{1}(t)=\frac{10}{10+20} i_{s}=e^{-t} \mathrm{mA}i_{2}(t)={2 e}^{-t} \mathrm{mA}
(b) v_{0}=L_{e q} \frac{d i_{s}}{d t}=\frac{20}{3} \times 10^{-3}\left(-3 e^{-t} \times 10^{-3}\right)=-20 e^{-t} \mu V
(c) W=\frac{1}{2} L i_{1}^{2}=\frac{1}{2} \times 20 \times 10^{-3} \times e^{-2} \times 10^{-6}={1.3534 \mathrm{nJ}}
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