Physics 313 Practice Test Page 1 University Physics III Practice Test II This practice test should give you a rough idea of the format and overall level of the Physics 313 exams. The actual exams will have different questions and problems, and may cover a different selection of topics. Individual questions and problems on the actual exams may be either harder or easier than those in this practice test. Assume that all numbers are significant to 3 figures. Formulas and constants: r E= r r F = qE ! r r qenc E • d A = # "0 k= ! melectron = 9.11"10#31 kg ! ! r r "V = # $ E • d s 1 Q rˆ 4 "#0 r 2 1 N m2 = 8.99 $10 9 2 4 "#0 C e = qelectron = 1.60 "10#19 C ! V= " ! Q = VC ! 1 U = Q "V 2 V = IR ! P = IV r #V ˆ #V ˆ #V ˆ E=" i " j " k #x #y #z ! ! k dq r Physics 313 Practice Test Page 2 1. A thin, uniformly charged ring of radius R and total charge Q is in the xy-plane, centered on the origin as shown. Point P is located on the z axis at (0, 0, z). (a) By direct integration, find the potential V (0,0,z) at point P as a function of z. y ! dq R x P (0, 0, z) z (b) Using therpotential function V (0,0,z) that you found in part (a), determine the components of the electric field E(0,0,z) at point P. ! ! Physics 313 Practice Test Page 3 (2) (a) I build 4 circuits (A, B, C, and D) out of resistors and capacitors as shown. These circuits are all built out of identical capacitors and identical resistors, but I don’t know the specific values of R and C. At t=0, a potential V is put across each of the circuits (separately) and held for a long time. Are the following statements True or False? _____ At t = 0, the initial current through one of the resistors in circuit C is half the current through the resistor in circuit A. _____ The final charge on each of the capacitors in circuits A and C will be the same. _____ The final charges on the individual capacitors in circuit D will be 3 times that of circuit A. _____ Ultimately, the potential difference across each individual capacitor in circuit C will be 3 times the potential across each capacitor in circuit D (b) A series RC circuit is made up of a 200. µF capacitor, a 400. kΩ resistor and a 12.0V battery with an internal resistance of 10.0 kΩ. At t =0.00 sec, a switch is closed, completing the circuit and starting to charge the (initially uncharged) capacitor. (i) Calculate the initial terminal voltage of the battery. (ii) How many seconds does it take for the instantaneous power dissipated by the resistor to fall to 50.0% of its initial value? Physics 313 Practice Test Page 4 (3) (Part 1) The following are actual answers given by Physics 313 students. Write the letters of the sentences that correctly explain why charge is uniformly distributed on the outer surface of an isolated spherical conductor. (Note: GL stands for Gauss’s Law) A. Due to GL the charge cannot be contained within the gaussian surface. B. GL says the charge enclosed must equal zero, and it is evenly distributed since the charges repel. C. Because it is static, charge cannot move, and the farthest away from each other the charge can get is on the surface. D. Conductors distribute charge evenly. E. GL says E = 0 since otherwise the conductors would spread the charge and would no longer be electrostatic. F. Like charges repel, pushing the charge through the whole of the material. G. The electric field inside the metal must be zero, and the charge is evenly distributed. H. Because the total charge inside is zero. The gaussian surface on the inside pushes the charges to the surface. I. GL says so! J. Since like charges repel, and electrons move freely in a conductor, the charges move as far from each other as possible. K. If it were not evenly distributed, there would be a repulsive force and E would not be zero. (Part 2) A 10 µF capacitor is charged by connecting it to a 12 V source. A 20 µF capacitor is separately charged to 15 V. (a) Calculate the charge on each capacitor and the energy stored in each capacitor. The capacitors are now disconnected from their sources and connected to each other with positive plate to positive plate, and negative plate to negative plate. (b) Find the effective capacitance of this combination. (c) Determine the potential difference across this combination. (d) What is the total energy stored in this combination? (e) Suppose the experiment is repeated but the capacitors are instead connected positive to negative and negative to positive. How do you expect the answers to parts (c) and (d) to change and why? Physics 313 Practice Test Page 5 (4) For the following circuit, find the three currents i1, i2, i3. Use the currents as defined on the figure. Calculate Va – Vb . PART II ON NEXT PAGE Physics 313 Practice Test Page 6 1b. Each of the resistors below has a value of 150 Ω. What is the effective resistance of the circuit?