2. Consider the following circuit: R₁ Vi(t) V₁(t) ₁ i₁(t) IL(S) c. From your answer to part (b), find V;(s). > R₂ Assume the switch is closed at t = 0, and for t < 0, iz(t) = 0. a. Find a differential equation governing the behavior of il(t). VL(S) b. In the Laplace domain find the transfer function: V¡(s).

Introductory Circuit Analysis (13th Edition)
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2. Consider the following circuit:
R₁
ww
Vi(t)
+
V₁(t)
il(t)
MM
Assume the switch is closed at t = 0, and for t < 0, iz(t) = 0.
a. Find a differential equation governing the behavior of i(t).
VL(S)
b. In the Laplace domain find the transfer function: V;(s).
R₂
IL(S)
c. From your answer to part (b), find V¡(s).
d. Given the switch closes at t = 0), find I£(s). (Like in problem 2, for this part,
treat V(t) as a constant voltage, V₁, and let V(s) = V₁/ s.)
e. Invert IL(s) to find iz(t).
f. Show that i(t) satisfies the differential equation from part (a) for t > 0.
Transcribed Image Text:2. Consider the following circuit: R₁ ww Vi(t) + V₁(t) il(t) MM Assume the switch is closed at t = 0, and for t < 0, iz(t) = 0. a. Find a differential equation governing the behavior of i(t). VL(S) b. In the Laplace domain find the transfer function: V;(s). R₂ IL(S) c. From your answer to part (b), find V¡(s). d. Given the switch closes at t = 0), find I£(s). (Like in problem 2, for this part, treat V(t) as a constant voltage, V₁, and let V(s) = V₁/ s.) e. Invert IL(s) to find iz(t). f. Show that i(t) satisfies the differential equation from part (a) for t > 0.
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