Beginnings and Endings

The questions below are due on Monday April 28, 2025; 10:00:00 PM.

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In the network shown below, the inductor and capacitor have zero current and voltage, respectively, prior to t = 0. At t = 0, a step in voltage from 0 to V_o is applied by the voltage source as shown.

where V_s(t) = \begin{cases}0 & \text{if}~t<0\\ V_o & \text{otherwise}\end{cases}

Find the following terms just after the step at t=0. Use V_o (with a little lowercase o, not a zero) for V_o, and use R, L, and C as needed.

v_C(0^+) =~

v_L(0^+) =~

v_R(0^+) =~

i(0^+) =~

{{\rm d}i\over {\rm d}t}(0) =~

Now find the following terms as t\to \infty:

v_C(\infty) =~

v_L(\infty) =~

v_R(\infty) =~

i(\infty) =~

{{\rm d}i\over {\rm d}t}(\infty) =~