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.   

Let us have a particle which is moving with a constant velocity v in the laboratory frame. Suppose this particle has a rest mass m and it decays into two photons.

We have to find an expression of the energy of the emitted photons as function of the angle between initial particle direction and the photons propagation direction

A light bulb is connected to a 60-V wall socket. The current in the bulb depends on the time t according to the relation I = (1.414 A) sin[(282.6 Hz)t].

(a) What is the frequency of the alternating current? Hz

(b) Determine the resistance of the bulb's filament? Ω

(c) What is the average power delivered to the light bulb? W