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Sample Final exam for PHY251

Questions (10 points each): Please blacken the letter of the best answer for each question.
Q1 An ideal 10 V battery connected across a resistor generates 1000 J in 20 seconds. The value of the resistor is
a) 1 Ohm.
b) 2 Ohms.
c) 50 Ohms.
d) 100 Ohms.		 Q2 A parallel plate capacitor is connected to a battery until it is fully charged, it is then disconnected, and the plates are pulled apart such that their separation is doubled. Which of the following statements is true?
a) The charge on the capacitor and the energy stored in it both increase.
b) The charge increases but the energy remains the same.
c) The energy increases but the charge remains the same.
d) The charge and the energy both remain the same.
Q3 A wire carries 10 amps from north to south. An electron is located directly below the wire and is traveling straight up. The force on the electron is
a) To the North
b) To the South
c) To the East
d) To the West
e) Zero
f) None of the above		 Q4 For a circuit design, an engineer wants to choose an inductor that will store 30 mJ of energy when it is carries a current of 5 A. What value inductor should she use?
a) 1.5 mH
b) 2.4 mH
c) 4.0 mH
d) 6.7 mH
e) None of the above
Q5 A heat engine operating between 27 °C and 327 °C is 3/4 as efficient as a Carnot engine operating between the same temperatures. Its efficiency is
a) 6%
b) 69%
c) 38%
d) 50%		 Q6 In process #1, two moles of a diatomic ideal gas at room temperature and one atmosphere are heated to a temperature of 600 K at constant pressure. In process #2, two moles of the same gas at the same initial conditions are heated to 600 K at constant volume. Which of the following is true?
a) Process #1 requires more heat
b) Process #2 requires more heat
c) The two processes require the same amount of heat
d) There is not enough information to decide which process requires more heat


Thermodynamics Problems (40 ponts each): Please do 2 of the following 3 problems. You must show your work. Credit will be awarded only for answers accompanied by correct work.
P1 An 0.1 kg copper vessel at 90 °C contains 1.8 kg of water, also at 90 °C. A piece of ice of mass 0.3 kg at T=-20 °C is added and the container is sealed.

Please find the final temperature of the system.

Useful data:
The specific heat of copper is 390 J/kg-K
The specific heat of water is 4190 J/kg-K
The specific heat of ice is 2000 J/kg-K
The latent heat of fusion of water is 334,000 J/kg
The latent heat of vaporization of water is 2,256,000 J/kg
P2 3.5 moles of a monatomic ideal gas are at P = 3.5 x 105 Pa in a volume of 0.025 m3. The gas expands adiabatically to 0.05 m3. Please find

a) The initial and final temperature of the gas.
b) The change in internal energy of the gas.
c) The final pressure of the gas.
d) The work done by the gas.
P3 Three moles of an ideal diatomic gas begin at volume V = 0.065 m3 and 1 atmosphere. The gas is taken through the following cycle.
  1. Volume doubled at constant pressure
  2. Pressure reduced by a factor of two at constant volume
  3. Volume reduced by a factor of two at constant pressure
  4. Pressure doubled at constant volume
a) Draw a P-V diagram for this cycle
b) Calculate the heat, work, and change in internal energy for each of the four processes.
c) Calculate the total heat, work, and change in internal energy for the whole cycle.
Other Problems (40 ponts each): Please do 4 of the following 5 problems. You must show your work. Credit will be awarded only for answers accompanied by correct work.
P4 Three parallel wires carry currents of I1, -2I1, and I1. The wires are located in the x-y plane, and run parallel to the y axis at x = -1, 0, and 1 as shown in the figure.

a) Give an expression for the magnetic field to the right of all the wires (x greater than 1).
b) Give an expression for the force per meter on the wire at x = -1.
P5 A solid insulating sphere of radius a carries a total charge Q as a uniform charge density (rho = Q/V = Q/(4/3)pi a3. Concentric with this sphere is a conducting spherical shell with inner radius b and outer radius c. The conducting shell carries a charge 2Q.

a) Find the electric field in each of the regions: r less than a, r between a and b, r between b and c, and r greater than c.
b) Find the surface charge density on the inner and outer surfaces of the spherical shell.
c) Find the potential differnce between the outer surface of the sphere and the inner surface of the shell.

P6 Consider a series RLC circuit. The source supplies a current of I=15cos(120 t) amperes. The values of the circuit elements are R = 30 Ohms, L = 175 mH, and C = 75 microfarads.
Please find
  1. The capacitive reactance
  2. The impedance
  3. The phase angle between V and I
  4. The average power delivered by the source.
  5. The maximum energy stored in the inductor
P7 A small styrofoam sphere of mass 0.2 g and charge 0.6 C is initially at rest at the origin. At t = 0, an electric field of magnitude 200 V/m is applied directed in the z-direction. After two seconds, the field is shut off.
You may ignore gravity and air resistance. Please answer the following questions.
  1. What is the acceleration of the charge while the field is turned on?
  2. What is the location of the charge at t = 3 seconds.
  3. What is the kinetic energy of the charge at the moment the field is turned off?
  4. After coasting for a while, the charge enters a magnetic field of magnitude 0.15 T directed in the x-direction, what will be the radius of curvature of the particle's path
P8 A 10 mF capacitor, a 10 V battery, a 100 Ohm resistor and a switch are connected in series. At t = 0, the switch is closed. Please find
  1. The current just after the switch is closed.
  2. The current a long time later.
  3. The voltage across the capacitor after 1 second.
  4. The energy stored in the capacitor after 1 second.
Other types of problems to look out for: Ampere's law, Faraday's Law, dc circuits, mirrors, lenses, prisms, the Biot-Savart law, E fields of charge distributions, RL circuits, and statics problems involving electric forces. Your best guides are the problems worked out in recitation and the test prep problems.
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