Estimate the overall uncertainty for this system using the

Question

Ohm's Law & Kirchoff's Law Review, & Measurement Method Concepts

1. Consider the circuit below, where current is driven by two voltage sources, one which is a known 18 V and another which is an unknown vx. Plot (on an appropriate scale) the resistance RA as a function of I1 in the range 0.001 A ≤ I1 ≤ 20 A.

2. The circuit depicted below contains a capacitor and voltage source.

(a.) If the capacitor is initially at zero charge, plot the current passing through the 30 Ω and 300 Ω resistors as functions of time.

(b.) If the voltage source is suddenly disconnected (as shown below), plot the current through the 30 Ω and 300 Ω resistors as functions of time.

3. Consider the modified bridge system depicted below (which is similar to a Wien Bridge), containing fixed resistances of magnitude R, an applied DC voltage V₁, a variable resistor RS, and a measured voltage V₂, to determine an unknown resistor and capacitor. If the capacitor is initially uncharged, in terms of the other parameters provided (including R_x and C_x), what must be the value of RS be for V₂ to be zero at all times? Show your derivation, and your answer may be a function of time, t.

4. Show how the following functions can be transformed into linear curves of the form Y = a₁X+a_o (i.e. determine Y, X, a₁ and a₀)
a. y = bx^m
b. y = be^mx
c. y = b + c*x^1/m

5. A force measurement system (i.e. a scale) has the following specifications: Range: 0 to 1000 N

Linearity Error: 0.10% Full Scale Output (FSO) Hysteresis Error: 0.10% FSO

Sensitivity Error: 0.15% FSO Zero Drift: 0.20% FSO

Estimate the overall uncertainty for this system, using the maximum possible FSO in your computations. What would the uncertainty be if the hysteresis error were removed?

6. The drag force (F_D) on a particle moving through a gas at low speed is found to be linear proportional to its speed relative to the gas(v) , i.e. F_D = -f_v. f is called the friction factor, and has units of kg s^-1. Measurements of f are carried out as a function of gas molecule mass (m_g, in kg per molecule), gas thermal energies (kT, the product of Boltzmann's constant and the temperature in Joules), mass densities, ρ_gas (kg m^-3), and dynamic viscosities (μ, in Pa s) for spherical particles of different radii, r_p. Data are provided in Table 1.

Table 1. A summary of friction factor measurements for variable radii particles under variable gas conditions.

Particle Radius (mm)	Thermal Energy (J)	Gas Density (kg m-3)	mgas (kg)	Viscosity (Pa s)	Friction factor (kg s-1)
1.00	4.14x10-21	1.05	4.78 x10-26	1.82 x10-5	3.13 x10-10
1.00	5.52 x10-21	0.79	4.78 x10-26	2.00 x10-5	3.37 x10-10
1.00	1.10 x10-20	0.39	4.78 x10-26	2.52 x10-5	3.92 x10-10
0.10	4.14x10-21	1.05	4.78 x10-26	1.82 x10-5	1.70 x10-11
0.10	5.52 x10-21	0.79	4.78 x10-26	2.00 x10-5	1.63 x10-11
0.10	1.10 x10-20	0.39	4.78 x10-26	2.52 x10-5	1.36 x10-11
0.01	4.14x10-21	1.05	4.78 x10-26	1.82 x10-5	2.63 x10-13
0.01	5.52 x10-21	0.79	4.78 x10-26	2.00 x10-5	2.30 x10-13
0.01	1.10 x10-20	0.39	4.78 x10-26	2.52 x10-5	1.65 x10-13
1.00	4.14x10-21	1.05	7.31 x10-26	3.00 x10-5	4.74 x10-10
1.00	5.52 x10-21	0.79	7.31 x10-26	3.30 x10-5	5.00 x10-10
1.00	1.10 x10-20	0.39	7.31 x10-26	4.16 x10-5	5.44 x10-10
0.10	4.14x10-21	1.05	7.31 x10-26	3.00 x10-5	1.75 x10-11
0.10	5.52 x10-21	0.79	7.31 x10-26	3.30 x10-5	1.60 x10-11
0.10	1.10 x10-20	0.39	7.31 x10-26	4.16 x10-5	1.23 x10-11
0.01	4.14x10-21	1.05	7.31 x10-26	3.00 x10-5	2.18 x10-13
0.01	5.52 x10-21	0.79	7.31 x10-26	3.30 x10-5	1.90 x10-13
0.01	1.10 x10-20	0.39	7.31 x10-26	4.16 x10-5	1.35 x10-13

(a.) Using Buckingham Pi type analysis, identify two or more dimensionless parameters which can be used to describe the independent variable, and the dependent variable (the friction factor).

(b.) The mean free path of a gas, A (in meters), defined as the average distance gas molecules travel between collisions with gas molecules, plays a role in determining the drag on nanoparticles. It is proportional to the ratio: (μ/ρ_gas )(m_gas/kT)^1/2, hence for non-dimensionalization this ratio can be used in lieu of the mean free path. Using only the friction factor, particle radius, viscosity, and the ratio (μ/ρ_gas )(m_gas/kT)^1/2 as variables, develop two dimensionless ratios, one to represent the independent variable, and a second for the dependent variable. Why are only two dimensionless ratios required to examine this system?

(c.) Plot, on appropriate axes, the dependent variable in (b.) as a function of the independent variable. Do all the data collapse to a single function?

7. On the following page, Table 2 displays results of heat flow experiments where two different fluids were used to cool flat plate electronic chips. The measured heat flow, equivalent to the product of the chip area, the convection coefficient, and the difference in temperature of the plate and fluid upstream temperature, was converted simply to the convection coefficient (units of W m^-2 K^-1) after experiments, and was reported as a function of the plate length (the plates were squares), fluid kinetmatic viscosity (the viscosity divided by the density), the fluid thermal diffusivity (the fluid thermal conductivity divided by the fluid density and specific heat), and the fluid thermal conductivity.

(a.) How many dimensionless ratios are needed to describe the dependent variable (the convection coefficient, h) as a function of the independent variables? Define these ratios, and also define symbols for each dimensional variable in the table. Create a table listing the values of all dimensionless parameters calculated based on the results in Table 2.

(b.) The different fluid experiments can be distinguished from one another in Table 2 by the different fluid properties provided. For each fluid, is one of the independent dimensionless ratios determined in a constant? If not, perform an alternative non-dimensionalization such that one of the independent dimensionless ratios is a constant for a given fluid.

(c.) Using the dimensionless ratios in (b.), summarize all results in a plot of the independent variable's dimensionless ratio and a single dependent variable's dimensionless ratio. You may use separate plots for different fluids. Be sure to use appropriate axes on plots.

Table 2. A summary of the measured convection coefficients for heat transfer from test electronic chips (flat plates), as functions of the plate length, upstream average velocity, working fluid kinematic viscosity, working fluid thermal diffusivity, and working fluid thermal conductivity.

Plate Length (m)	Upstream Velocity (m s-1)	kinematic viscosity (m2 s-1)	Thermal diffusivity (m2 s-1)	Thermal conductivity (W m-1 K-1)	Convection Coefficient (W m-2 K-1)
0.010	0.0100	1.5 x10-5	1.9 x 10-5	0.026	4.60
0.010	0.0120	1.5 x10-5	1.9 x 10-5	0.026	5.14
0.010	0.0144	1.5 x10-5	1.9 x 10-5	0.026	6.50
0.010	0.0173	1.5 x10-5	1.9 x 10-5	0.026	5.95
0.010	0.0207	1.5 x10-5	1.9 x 10-5	0.026	8.22
0.010	0.0249	1.5 x10-5	1.9 x 10-5	0.026	9.32
0.010	0.0299	1.5 x10-5	1.9 x 10-5	0.026	9.20
0.010	0.0358	1.5 x10-5	1.9 x 10-5	0.026	11.1
0.010	0.0430	1.5 x10-5	1.9 x 10-5	0.026	11.7
0.005	0.0100	1.0 x 10-6	1.4 x 10-7	0.610	1670
0.005	0.0120	1.0 x 10-6	1.4 x 10-7	0.610	1994
0.005	0.0144	1.0 x 10-6	1.4 x 10-7	0.610	2185
0.005	0.0173	1.0 x 10-6	1.4 x 10-7	0.610	2579
0.005	0.0207	1.0 x 10-6	1.4 x 10-7	0.610	2977
0.005	0.0249	1.0 x 10-6	1.4 x 10-7	0.610	3036
0.005	0.0299	1.0 x 10-6	1.4 x 10-7	0.610	3414
0.005	0.0358	1.0 x 10-6	1.4 x 10-7	0.610	3771
0.005	0.0430	1.0 x 10-6	1.4 x 10-7	0.610	4584
0.005	0.0516	1.0 x 10-6	1.4 x 10-7	0.610	5044
0.005	0.0620	1.0 x 10-6	1.4 x 10-7	0.610	6432

Garrett p. 56 Case Study #2

Garrett, T., Baillie, H., & Garrett, R. (2013). Health care ethics: Principles and problems (6th ed.). Upper Saddle River, NJ: Prentice Hall.

You will be graded based on your presentation of the case study and participation in the discussion of other's presentations. Participation in the discussion is a very important aspect of this assignment. In order to have adequate time to participate in the discussion, your initial presentation should be posted no later than Thursday 8AM. That will allow the remainder of the week for discussion. You may respond to another classmates as soon as it is posted, you don't have to wait until Thursday. It is expected that the required responses will be posted in a timely manner. If you cannot post your case presentation by Thursday AM, or your required response will be late, you must let me know ahead of time to avoid loss of points.

As the presenter, you should include a brief description of the case, issues within the case, and some analysis. The questions at the end of each case study are there to stimulate discussion among your group. As a presenter you are not required to answer the questions as part of your presentation. Be sure you do read the guidelines and grading rubric in order to understand the criteria for this assignment

Ethical Case Study Guidelines

OVERVIEW:
Discussions are a very important aspect of online classes, because they allow you to apply the content of the course to specific situations or problems, as well as allow group discussion and interaction. You will be assigned to present and respond to various ethical case studies four times throughout the semester. For this activity the class will be divided into groups of seven or eight. Each of you will be assigned a specific case to present and discuss. The following guidelines outline the requirements of the assignment. In addition to your case discussion, you will also need to provide substantive and thoughtful responses to at least two (2) presentations by other members of your group.

For example, you may be directed to present "Case Study # 1, from Chapter 2 of Garrett pg. 51". In addition, you will need to respond at least two of your group's presentations - more than 2 responses are preferred and encouraged.

CRITERIA:
When you present the case study, you will do so in the "Discussion" section of the respective Focus. The presentation of your assigned case should be posted by 8 AM on Thursday in the week it is due. By posting the presentations mid week, it will allow each of you to respond to other's presentation throughout the remainder of the week. The following should be included in your presentation and responses:

Presentation: Your presentation of the assigned case study is worth over half of the possible points in each case study and should include the following information:

1. The page number & case number of the case study,

2. A BRIEF, but sufficient overview of the case study to enable readers to understand the facts and issues of the case. Your overview should be complete enough that the others in your group will understand the facts and issues of the case. When you are writing your presentation I would suggest you compose it in Word and then copy and paste it into the response area on e-college, rather than try to compose it in the discussion area.

3. You should identify what you see as the relevant ethical issues presented by the facts.

a. Your discussion should include an analysis of how the ethical principles discussed in your text and lectures relate to the issues.

b. When relevant, discuss how these ethical principles may apply to the various individuals involved, e.g. patient, family, physician, care givers, etc.

c. You will probably have a strong feeling one way or the other about these cases, but I want you to step back and look at these issues from all the stakeholders positions

and try not to be influenced by your own moral or personal views. That does not mean you can't express your opinion, but when you do, be sure it is based on an ethical or legal theory or principle and discuss how your position is supported by those principles or theory.

d. There will generally be questions at the end of each case study, they are there to stimulate discussion - as the presenter, you are not required to answer these questions specifically. They may help you in formulating your own discussion or responding to other's presentations.

4. References:

a. You are encouraged to use your texts for this course as references for your discussion. However, in addition to your text you must also utilize three other references. The additional references should include at a minimum (1) one reference for your own case presentation and (2) two references for your responses to other postings. You may to cite your text, but it does not count toward the three new references you should find. (That means you should include a minimum of three new references to the threaded discussion each week).

b. Cite your references at the end of your presentation or discussion.

c. Follow APA formatting for your references as best you can. You will not be graded on the "correctness" of your APA citations, but put forth your best effort so others may access your references. If you accessed your references online, then post the link so other student's may also access those references.

5. I am not looking for long detailed discussions of these cases (you don't have to address every possible issue), but you should at least identify the main themes. This is not like an essay test question. After all, you do want to leave something for your classmates to say

6. All postings should reflect clarity of writing, correct grammar and spelling.

Reference: APA