A Fresh State of Mind

The questions below are due on Tuesday October 14, 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?)

If 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) =~

If 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.

If 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) =~

If 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) =~