Electrical Circuits Homework

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ECE102_HW-a2_W2018.pdf

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ECE 102 ENGINEERING COMPUTATION

ANALYSIS HOMEWORK #2

ECE DEPARTMENT PORTLAND STATE UNIVERSITY

WINTER 2018

ECE 102 Analysis Homework #2 Winter 2018

ECE 102 Analysis Homework #2 (HW-a2)

Problem List

10 pts Problem #1 - Significant figures

15 pts Problem #2 - Unit conversions

10 pts Problem #3 - Analysis: Ships leaving port

10 pts Problem #4 - Analysis: Tower height

10 pts Problem #5 - Analysis: Animals in a field

20 pts Problem #6 - Analysis: Resistor sig figs and min/max

20 pts Problem #7 - Analysis: Tubes

5 pts Following presentation format rules

General Instructions

For Problems #1 through #7:

• Unless told otherwise, you must show your equations and calculations to get full credit.

• Unless told otherwise, express numeric answers to the correct number of significant figures.

• Solutions MUST be either hand-written on engineering paper or printed out using a computer. Failure to follow this rule will result in a zero score for the homework.

• Follow the presentation format discussed in the “Problem Solving” lecture.

o For Problems #1 and #2, no Diagram, Solution Check, or Discussion is needed.

o For Problems #3, #4, #5, #6, and #7, include all of the standard presentation sections.

• Either draw a double underline beneath or box the final answers you want graded.

• Staple your paper sheets together.

• Submit your solutions to the instructor at the beginning of class on the due date.

ECE 102 Analysis Homework #2 Winter 2018

Problem #1

Assume the following numbers (except for π) are measured values in some unit system.

For Parts (a) through (e), state the number of significant figures for each numeric value.

a) 6.210

b) 0.001050×10-2

c) 270

d) 10101010

e) 0332700.

For Parts1 (f) through (j), perform the requested calculations and report the answers with the

correct number of significant figures.

f) (8.14)(260)

g) 456 / 4.9

h) (6.74)(41.07) / 4.13

i) (10.78 – 4.5) / 300

j) (2π – 5) / 10.

1 From ECE 102 Engineering Computation (PSU Edition), K. Hagen: “Analysis Methodology”, Prob 11.

ECE 102 Analysis Homework #2 Winter 2018

Problem #2

Perform the following unit conversions2. To get credit, show your conversion factors!

Assume numbers are measured. Express your results to the correct number of significant figures.

a) A world-class sprinter can run 100. m in a time of 9.80 s, an average speed of 10.2 m/s. Convert this speed to mi/h.

b) The typical home is heated by a forced-air furnace that burns natural gas or fuel oil. If the heat output of the furnace is 175,000 Btu/h, what is the heat output in units of kW?

c) A copper tube carries hot water to a dishwasher at a volume flow rate of 3.0 gal/min. Convert this flow rate to units of m3/s and ft3/h.

d) A symmetric I-beam of structural steel (ρ = 7860. kg/m3) has the cross section shown in Figure P2. Calculate the weight per unit length of the I-beam in units of N/m and lbf/ft.

Assume the local gravitational constant is g = 9.81 m/s2.

2 From ECE 102 Engineering Computation (PSU Edition), K. Hagen: “Dimension and Units”, Probs 19, 21, 38, 25.

350. mm

30.0 mm

40.0 mm

Figure P2

Sample I-beam

ECE 102 Analysis Homework #2 Winter 2018

Problem #3

A ship leaves port at 12:00 P.M. (noon) and sails east at 10.0 miles per hour. Another ship leaves

the same port at 1:00 P.M. and sails north at 20.0 miles per hour.

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At what time (i.e., on the clock) are the ships 50.0 miles apart?

ECE 102 Analysis Homework #2 Winter 2018

Problem #4

At a certain Point A on level ground, the angle of elevation to the top of a tower is observed to be

33.0°. At another Point B, in line with A and the base of the tower and 50.0 feet closer to the tower, the angle of elevation to the top is observed to be 68.0°.

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What is the height (in feet) of the tower?

ECE 102 Analysis Homework #2 Winter 2018

Problem #5

In a field there are cows, birds, and spiders. Spiders have four eyes and eight legs each. In the

field there are 20 eyes and 30 legs. All three animals are present, and there is an odd number of

each animal.

How many cows, birds, and spiders are present?

NOTE:

You could probably “brute-force” guess the solution to this problem, but that is not acceptable for

grading purposes. You are expected to present a logical progression of analytical steps, using the

constraints imposed by the problem statement, to prove your assertions of how many of each kind

of animal there is. At each step, justify why you made that particular choice.

ECE 102 Analysis Homework #2 Winter 2018

Problem #6

The schematic shows a simple combination of resistors that is connected to a DC voltage source

to form a complete circuit. I is the current flowing through the voltage source. The resistor and

voltage numbers in the table are only the average values as specified by the manufacturer. The

actual values can be anything within the tolerance range.

The equivalent resistance of the circuit is given by this equation: 32

32 41

RR RRR

eq + ++=

The equation for the current I is: eq

V I =

a) Create a table that shows the minimum and maximum values for each component b) What is the minimum value (in mA) that the current I can be? c) What is the maximum value (in mA) that the current I can be? d) Discuss how variations in manufacturing tolerances can affect the design and cost of a circuit.

R4 VDC

Value Tolerance

R1 10 Ω ± 5%

R2 150 Ω ± 10%

R3 330 Ω ± 10%

R4 220 Ω ± 20%

VDC 5 V ± 5%

ECE 102 Analysis Homework #2 Winter 2018

Problem #7

Your company manufactures tubes made of different materials. A tube is a hollowed out cylinder

of length L and outer diameter D. The walls of the tube have a uniform thickness t. The tube

material has density ρ.

For the following calculations, assume the local gravitational acceleration constant is 9.81 m / s2.

a) Calculate the mass in kilograms (kg) of a copper tube with these specifications: L = 72.10 inches long, D = 8.55 cm, t = 4.0 mm, ρ = 8.96 g / cm3.

b) Calculate the weight in newtons (N) of a lead glass tube with these specifications: L = 1250 mm long, D = 5.0 cm, t = 10.5 mm, ρ = 1.648×105 g / ft3.

c) Calculate the weight in pounds-force (lbf) of a brass tube with these specifications: L = 3.25 m long, D = 4.00 cm, t = 0.125 inches, ρ = 8.5×103 kg / m3.

L t