LC and some switches (I)

The questions below are due on Monday November 25, 2024; 10:00:00 PM.

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The circuit shown below includes two switches: S1 and S2. Prior to t = 0, both switches are open, and the capacitor voltage v(t) and inductor current i(t) are both zero.

At t = 0, S1 closes, and it remains closed until t = T_1. Determine i(t) and v(t) for 0 \leq t \leq T_1.

Use T_1, T_3, and T_4 for T_1, T_3, and T_4, respectively as needed in this problems various parts. In addition, use pi for the constant \pi. You can use the standard trigonometric functions sin(arg), cos(arg), tan(arg), and inverse functions asin(arg), acos(arg), and atan(arg). You can use sqrt(arg) or do the root explicitly in python arg\*\*0.5.

Part A

Enter an expression for v(t) for 0 \leq t \leq T_1.
v(t)=

Enter an expression for i(t) for 0 \leq t \leq T_1.
i(t)=

Part B

At t = T_1, S1 opens as S2 simultaneously closes; the two switches change states so that they are not closed at the same time. The switches remain in their states until i(t) goes to zero, at which time S2 opens. Define the time at which i(t) goes to zero as t = T_2. Determine T_2, as well as i(t) and v(t) for T_1 \leq t \leq T_2.

Enter an expression for i(t) for T_1 \leq t \leq T_2.
i(t)=

Enter an expression for v(t) for T_1 \leq t \leq T_2.
v(t)=

Enter an expression for T_2.
T_2=

Part C

Both switches remain open until t = T_3. Determine v(t) and i(t) for T_2 \leq t \leq T_3.

Enter an expression for v(t) for T_2 \leq t \leq T_3.
v(t)=

Enter an expression for i(t) for T_2 \leq t \leq T_3.
i(t)=

Part D

At t = T_3, S1 again closes, and it remains closed until t = T_4. Determine i(t) and v(t) for T_3 \leq t \leq T_4.

Enter an expression for v(t) for T_3 \leq t \leq T_4.
v(t)=

Enter an expression for i(t) for T_3 \leq t \leq T_4.
i(t)=

Part E

Finally, at t = T_4, S1 opens as S2 again simultaneously closes. The switches remain in their states until i(t) again goes to zero, at which time S2 opens. Define the time at which i(t) again goes to zero as T_5. Determine T_5, as well as i(t) and v(t) for T_4 \leq t \leq T_5.

Enter an expression for i(t) for T_4 \leq t \leq T_5.
i(t)=

Enter an expression for v(t) for T_4 \leq t \leq T_5.
v(t)=

Enter an expression for T_5.
T_5=