first-order transient circuit
  • Inductors are best solved by considering the current flowing through the inductor.
  • We combine the resistive element and the source into a Norton Source Circuit.
  • We apply KCL
    • $i_{source}(t)=\frac{L}{R}\frac{di_{inductor}(t)}{dt}+i_{inductor}(t)$
  • Solution
  • $x(t)=K_1+K_2e^{-\frac{t}{\tau}}$
      • $K_1$:steady-state solution, $\tau$:time constant
      • The circuit approaches steady-state on 5$\tau$.
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