2. Assume that the potential in Cartesian coordinates is given as V=x²-y². According to this;

(a) The value of the potential at coordinate P (2, -1,3)

(b) Electric field, the magnitude of the displacement vector and field lines

(c) Calculate the charge density on the conductive surface

1- A 9 V battery is powering a simple circuit with one light bulb. There is a current of 0.58 running through the bulb and a voltage drop of 5.8 across the bulb. What is the internal resistance of the battery?

2- A series circuit uses three resistors. One resistor has a resistance of 19 Ω. The second resistor has a resistance of 26 Ω. The final resistor has a resistance of 21 Ω. What is the equivalent resistance of this circuit?

3- A parallel circuit consists of two resistors in parallel. The first resistor has a resistance of 17 Ω and the second resistor has a resistance of 57 Ω.  What is the equivalent resistance of this circuit?

4- Which of the following are true about using an ammeter in a circuit?

4- in a _____________ circuit, the components are connected in a single line. If more resistors are added to this circuit, then total current _________ and the equivalent resistance ___________ compared to the original circuit. in a __________ circuit, the components are connected in branches. If more resistors are added to this circuit, then the total current ____________ and the equivalent resistance ____________ compared to the original circuit.

options: series, decreases, remains unchanged, parallel, incomplete, increases

1. If you connect a 9 v battery up to a 7 Ω resistor and a 10 μF capacitor for a very long time, what would the current in the circuit be?

2. What is the time constant in an RC circuit and how is it found?

3. In your own words what is meant by an RC circuit and give an example of one you might find in the real world.

For the following u(x, y), show that it is harmonic and then find a corresponding v(x, y) such that f(z)=u+iv is analytic.

u(x, y)=(x^2-y^2) cos(y)e^x-2xysin(y)ex

Near the surface of the Earth there is an electric field of about 150 V/m which points downward. Two identical balls with mass 0.407kg are dropped from a height of 2.29m , but one of the balls is positively charged with q1 = 338?C , and the second is negatively charged with q2=-338?C . Use conservation of energy to determine the difference in the speeds of the two balls when they hit the ground. (Neglect air resistance.)

In Griswold v. Connecticut, the U.S. Supreme Court stated that “specific guarantees in the Bill of Rights have penumbras, formed by emanations from those guarantees that help give them life and substance.”

1. Discuss the meaning and implications of Griswold’s penumbras and emanations

2. Describe the legal basis for an unenumerated right that might be located within these purported constitutional regions.

(a) Calculate the wavelength of an electron under an acceleration voltage of (i) 200 V, (ii) 1.5 MeV and (ii) 2.5 GeV. Also, calculate the velocity of electrons moving at these acceleration voltages. How does this velocity compare to the speed of light. If they are comparable to the speed of light, use relativistic effects to calculate the wavelength of electron?

(b) If the wavelengths are so small, can one expect the resolution of the TEM made with these energies to be so small? If not, what will be the reason behind those discrepancies.

A 2400-W oven is connected to a 240-V source.

1. What is the resistance of the oven?

Express your answer to two significant figures and include the appropriate units.

2. How long will it take to bring 110 mL of 25 ∘C water to 100∘C assuming 65 % efficiency? The specific heat capacity of water is 4186 J/(kg⋅∘C).

Express your answer using two significant figures.

3. How much will this cost at 12 cents/kWh?

Express your answer using two significant figures.

. Two outlets on the same household circuit (120 V) are connected in series, while the sockets in each are in parallel. In the first outlet you plug in a 100. W lightbulb and a 1200 W vacuum cleaner. In the second outlet you plug in another 100 W lightbulb and a 1500 W hairdryer.

(a) Draw a circuit diagram.

(b) Determine the current through each device.

(c) Determine the resistance of each and the equivalent resistance of the circuit.

(d) If the circuit has a 25 A fuse connected to it, will the fuse blow?

(v) Why are errors squared in a regression? a. to give more weight to smaller errors b. because summing positive and negative errors will cancel them out c. multiplying positive and negative errors will always result in negative numbers d. errors are not actually squared in a regression   

(vi) The best linear prediction rule is the one that has the least a. error when predicting from the mean. b. squared error when predicting from the mean. c. error when predicting using that rule. d. squared error when predicting using that rule.   

(vii) The sum of the squared errors when predicting from the mean is called a. SSError. b. proportionate reduction in error. c. SSTotal. d. proportion of variance accounted for.   

(viii) What is the formula for the proportionate reduction in error? a. (SSError – SSTotal) / SSError b. (SSError + SSTotal) / SSError c. (SSTotal – SSError) / SSTotal d. SSTotal / (SSError + SSTotal)

(ix) What does it mean when SSTotal minus SSError equals zero? a. This is the best case—it means there is zero error. b. This is the worst case—it means the prediction model has reduced zero error. c. The proportionate reduction in error is 50%. d. The underlying correlation is negative.   

(x) When drawing a regression line for a linear prediction rule, the minimum number of predicted points on a graph that must be located is a. 1. b. 2.   
Homework – Chapter 12. Student name:____________________
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c. 1 if it is a positively sloped line; 2 if it is a negatively sloped line. d. 2 if it is a positively sloped line; 1 if it is a negatively sloped line.