NuMeths - Final Oral Examinations

7/29/2019 NuMeths - Final Oral Examinations

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Final Oral Examinations Numerical Methods

1. (Electrical Engineering) A series RLC circuit has the following components: R 200 ,C 4.7 F, L 0.15 H and the voltage source is 100 V. Assume zero initial conditions.

a. Graph the response of the capacitor voltage for the given voltage source, using a circuit

simulator. What type of response (underdamped, overdamped, undamped, criticallydamped) is this?

b. What is the mathematical expression of this response?

c. Determine the peak value of the response and the time when the peak value is

achieved, using the graph obtained in (a) and applicable numerical methods.

d. The percent overshoot of a response is a parameter used to describe the transient

response of a system such as this electrical network. It is the percentage difference

between the peak value and the final value of the response. For this circuit, determine

the percent overshoot.

e. Interpret this percent overshoot value. How does overshoot affect the performance of a

circuit?

2. (Semiconductor Physics) The resistivity of doped silicon is based on the charge q on anelectron, the electron density n, and the electron mobility . It is given as

1qnThe electron density is given in terms of the doping density N and the intrinsic carrier density n,as in

n 12 N N 4nwhile the electron mobility is described by the temperature T, the reference temperature Tand the reference mobility , as in

TT.

Determine the required doping density when the desired resistivity is 6 . 5 1 0 V s

cm/Cusing the following parameters:

T

300 K,

T 1000 K,

1350 cm

/V s,

q 1 . 7 1 0 C and n 6.2110 cm. Use applicable numerical methods.

3. (Electrical Engineering) (a) For the circuit shown below, establish mesh current equations and

solve for the mesh current using applicable numerical method.


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(b) For the circuit shown below, determine node equations for nodes A, B and C with respect toD, and find the node voltages using applicable numerical methods.

4. (Strength of Materials) The data below were obtained from a creep test performed at room

temperature on a wire composed of 40% tin, 60% lead, and solid core solder. This was done by

measuring the increase in strain over time while a constant load was applied to a test specimen.

Using linear regression methods, find (a) the equation of the line that best fits the data, and (b)

the r value. Plot the discrete data below and superimpose the resulting regression line.


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(c) Does the line pass through the origin that is at time zero should there be any strain? If the

line pass does not through the origin, force it to do so. Does this new line represent the data

trend? Suggest a new equation that satisfies zero strain at zero time and also represents the

data trend well.

5. (Electromagnetics) A total charge Q is uniformly distributed around a ring-shaped conductorwith radius a. A charge q is located at a distance x from the center of the ring, as depicted in thefigure below. (a) Show that the magnitude of the force exerted on the charge by the ring is given

as

F 14eqQx

x a/ where e 8.8510 C/Nm. (b) Plot the force F as a function of the distance x. (c) Findthe distance x, using applicable numerical methods, where the force is 1 N if q and Q are2 1 0 C for a ring with a radius of0.9 m.


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Groupings:

Group A Group B Group C Group D Group E

Amado Aquino Caindoy Epres Espiritu

Cabatian Ison Jesoro Lagrimas Penales

Nofre Maming Martinez Rubaya Santos

Romero Mendoza Paroligan Sangcap Tugade

Sario Moreno Velasquez Susbilla Vargas

Guidelines and instructions:

1. The final oral examinations will be scheduled on Friday, March 16, 2012. Room is to be

announced. The schedule is as follows:

3:30 4:30 Group 1

4:30 5:30 Group 2

5:30 6:30 Group 36:30 7:30 Group 4

7:30 8:30 Group 5

Group numbers are to be determined via draw lots tomorrow.

2. There will be five problems, all engineering applications of the numerical methods for the

following problems: roots of equations, linear equations, optimization and curve fitting.

3. The group has to document the detailed solutions of the problems. Computer-aided methods of

solving are allowed. Submission of the document is on the schedule of the oral exams.

4. The group must prepare a presentation for the oral exams. It will be given 55 mins to present

everything, starting from the scheduled time. If the group was not able to present all the

problems, all problems that are not presented will be considered incorrect.

5. I reserve the right to determine the order of presentation and who will present what problem.

In any case, one person is to be assigned to present one problem.

6. Each problem is worth 20 points. The scores will depend on the correctness of the answer and

the manner by which it was presented by the presentor. Incorrectly solved problems, including

those that are not presented will receive 3 points. The official score will be total for each

problem.

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NuMeths - Final Oral Examinations