A Fresh State of Mind

The questions below are due on Monday March 17, 2025; 10:00:00 PM.

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1) Part 2

Each of the two networks that follows has a non-zero initial state at $t = 0$ (this is indicated for separately for each network). Find the network states for $t > 0$ .

(Hint: what equivalent resistance is in parallel with each capacitor, and what time constant results from this combination?)

v_{a} (0) = V

, what is

v_{a} (t)

for

t > 0

? Enter your answer as a Python expression involving V, R_1, R_2, and/or C. You may use exp(x) or e**(x) to represent

e^{x}

, and you may use ln(x) to represent the natural log of

x

.

For

t \geq 0

v_{a} (t) =

v_{b} (0) = V

, what is

v_{b} (t)

for

t > 0

? Enter your answer as a Python expression involving V, R_1, R_2, and/or C. You may use exp(x) or e**(x) to represent

e^{x}

, and you may use ln(x) to represent the natural log of

x

.

For

t \geq 0

v_{b} (t) =

2) Part 2

Each of the two networks that follows has a non-zero initial state at $t = 0$ (this is indicated for separately for each network). Find the network states for $t > 0$ .

i_{a} (0) = I

, what is

i_{a} (t)

for

t > 0

? Enter your answer as a Python expression involving I, R_1, R_2, and/or L. You may use exp(x) or e**(x) to represent

e^{x}

, and you may use ln(x) to represent the natural log of

x

.

For

t \geq 0

i_{a} (t) =

i_{b} (0) = I

, what is

i_{b} (t)

for

t > 0

? Enter your answer as a Python expression involving I, R_1, R_2, and/or L. You may use exp(x) or e**(x) to represent

e^{x}

, and you may use ln(x) to represent the natural log of

x

.

For

t \geq 0

i_{b} (t) =