Impulsive Behavior
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1) Part 1
The following circuit has an input that can be well-modeled as an impulse, v_1(t) = \lambda\times\delta(t), where \lambda has units of V\times s and \delta(t) is the impulse function discussed in lecture. Find v_{\rm C}(t) in the circuit below for times t>0, assuming that v_{\rm C}(0_-) = 0.
Enter your answer as a simple Python expression involving lambda, R_1,
R_2, C, t, and/or any other constants you need. You can use e**x or
exp(x) to represent e^x, and you can use ln(x) to represent \ln(x).
You may also use ser(x,y) and par(x,y) to represent series and parallel combinations of resistors, respectively.
2) Part 2
The following circuit has an input that can be well-modeled as an impulse, i_1(t) = Q\times\delta(t), where Q has units of Coulombs and \delta(t) is the impulse function discussed in lecture. Find v_{\rm C}(t) in the circuit below for times t>0, assuming that v_{\rm C}(0_-) = 0.
Enter your answer as a simple Python expression involving Q, R, C, t, and/or any other constants you need. You can use e**x or
exp(x) to represent e^x, and you can use ln(x) to represent \ln(x).
You may also use ser(x,y) and par(x,y) to represent series and parallel combinations of resistors, respectively.
