Question

i from q_01 Cross-sectiona Surface > It is unnecessary to include this document in your homework submittal. Given: 1. The charge, q(t), over 0 <t < y (seconds), is given by: q(t) = A+ Be 7 Coulombs. Refer to the lecture for the definition of q(t). 2. The constants A, B, T, and t\ are given in the parameter file for this problem. ECE 2010 H01 i from q_01 parameters.txt is found at the link "Parameters" near the top of the Homework Assignment Table 3. Refer to the document: 0 SIPrefixes Table.pdf in the Parameters directory to interpret the unit prefixes. Do: All calculations and plots in both parts a) and b) must be done manually. a) Plot q(t) in Coulombs over 0 <t < t seconds. It is not necessary to list the points in a table that you use for the plot You should (though not required to do so) put a dot on your plot for each point calculated and sketch by free-hand a smooth curve through those points. This part is worth 5 points out of the total available for this problem. You will need to plot many more than 5 points to produce a reasonably smooth curve!) b) Find i(t) i Amps over 0 < t < t, seconds. (This component, "Find", of part b) is worth 10 points) and plot i(t) in Amps over 0 < t < t, seconds by hand. (This component, "Plot", of part b) is worth 5 points.) The same recommendations for plotting in part a) apply here as well Express the answer to the "Find" part of b) as i(t) C+De-7 Amps 0< Seconds Over For example, if C = -4.3915 x 10-4, D = 840.008 x 10-5, 7 = 0.0063835 x 10-4, and if t is given as 2.5 usec, (Note that these numbers have all been made up only for demonstration purposes, and at this stage these numbers are not in the format required for the final answer.) then the final answer would be properly cxpressed (with the numbers that are shown in the cxprcssion in Engincering Numeral Format) as: t i(t)= -439.2 x 10- 8.4 x 10-3e 638.35 x 10-Amps 0t2.5 x 10- seconds over Be sure to follow the Homework Format and Plot Format requirements shown in the course syllabus web pages. There will be no second chances to recover points if you neglect to follow those requirements. If the requirements are ambiguous, then let me know. Otherwise, I will not "pre-check" your work before you submit it. See the next page for Hints.
A = -8nC

B = 11nC

tau = 6usec

t_1 = 30usec

Answer 1

q (t) = A + B e^-t/e, A = -8 n C, tau = 6 mu sec B = 11 nC, t_1 = 30 mu sec Therefore q (t) = -8 nC + (11 nC) e^-t/30 mu sec Therefore q (t) = (-8 + 11 e6-t/6 times 10^-6) times 10^-9 n rightarrow 10^-9 mu rightarrow 10^-6 over 0 lessthanorequalto t lessthanorequalto t i.e 0 lessthanorequaltot lessthanorequalto 30 mu sec for t = 0, q(t) = (-8 + 11 e^-0/06 times 10^-6) times 10^-9 (Because e^0 = 1) = (-8 + 11 (1)) times 10^-9 = 3 times 10^-9 = 3n C Therefore q(0) = 3n C for t = 3 mu sec, q(t) = (-8 + 11 e^-3 mu/6 mu) times 10^-19 = -1.32n C Therefore q(3) = -1.32 nC for t = 6 mu sec, q (t) = (-8 times 11 e^-6 mu/6 mu) times 10^-9 = -3.95 nC
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