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Question: q0 8 nc t0 3 msec i0 ...

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q-from-L01 Cross- securfuce It is unnecessary to include this document in your homework submittal Given: l. The current, i(1), ıs a piecewise linear function given by the set of points, (4 %) for 2. The initial value of q(t) at t-to, viz. go-q(to) 3. Values for the point pairs and q(to) are found in the parameter file for this problem -0, I, , ECE 2010 H01q from i 01 parameters.txt is found at the link Parameters near the top of the Homework Assignment Table 4. Refer to the document: 0_SI Prefixes_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) Fid i(1) in Amps over 10 < I < In seconds. (This component, Find, of part b) is worth 10 points) and plot i(t) in Amps over to S t tn seconds. (This component, Plot, of part b) is worth 5 points.). Expross your answer to the Find part in the following form i2(t) tl <t<t2 Amps seconds b) Find q(t) in Coulombs over to t< tn seconds, This part is worth 30 points out of the total available for this problem.) and plot q(t) in Coulombs over to S t tn seconds. (This component Plot, of part b) is worth 5 points.). Express your answer to the Find part in the following form q1(t) to<t<t g2(t) ti<t< t2 Ia (t) . tn-1 <t < tn .. Coulombs seconcls 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. Otherwisc, I will not pro-chcck your work before you submit it See the next page for Hints.

Hints: 1. Polynomials are found within many concepts in Electrical Engineering. You might need to review funda- 2. To produce the plot for i(t) simply connect the dots with straight lines between the given set of points 3. All the segments of i(t) are linear (1st order polynomials). Hence, each of them can be written using the mental algebra relationships involving polynomials along with the calculus associated with polynomials (tk,2k) for k 0,1, . . . , n expression of a straight line: i(t)-at bk Amps for the kth segment between (tk-1, ik-1) and (tk, ik) for k = 1, 2, , n. (Note that (to, io) is the starting point.) The slope is ak, and the vertical intercept at t = 0 is bk for each line segment 4. Use the relationship q(t) (t)dt i(tx)dti(tx)dtr, and the given initial value of q(t) at t-to to obtain the answer to Find q(t) in part b) 5. The para neter, to, shown as to is NOT equal to zero, i.e. toメ0. The parameter, q(10), shown as q0 . is NOT q(0) 6. The resulting expressions for q(t) can be constant, linear, or quadratic polynomials 7. For the Plot required in part b), the curve of q(t) will be different over different segments of time. It will either be a straight line or a parabola in each segment. In segments where q(t) is a parabola, it should appear smooth. You should be able to use your background in mathematics to determine if a parabola is concave up or down, etc. You could also compute several intermediate points between the end points of the parabola and sketch a curve through them freehand. It is not required that you list values in a table on your submittal that you used to render the plots

q0 = 8 nC

t0 = -3 msec

i0 = -2 uA

t1 = 1 msec

i1 = 6 uA

t2 = 5 msec

i2 = 3 uA

t3 = 10 msec

i3 = -9 uA

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