# LC and some switches, take 1

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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 T1 for Enter T_1, etc. 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

v(t)=

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.

i(t)=

v(t)=

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.

v(t)=

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.

v(t)=

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.

i(t)=

v(t)=

T_5=