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Exam 3 Apr. 4, 2002 Physics 212 Spring 2002 Name________________________ This 100-point exam consists of four questions with five parts each. If you cannot do one part, move on to the next. Partial credit will be given on all parts of this exam. This is a closed book exam. You will need a calculator. Please remember to write your name on every page. Remember to convert to meters and kilograms. To receive full credit, you must show all of your work or reasoning. At times, you may need to explain your reasoning in words. When grading I look for quality thinking more than right answers so do take the time to reason carefully. Please ask if the wording of a question is not clear to you. Energycap 12 CV 2 Equations: FE ,q qE Force on a charge, q P = IV Q V energy in a capacitor power E kq r2 point charge C E 2 o single plate 1 1 1 parallel ... R1 R2 Req V kq r potential—point charge or 1 1 1 ... C1 C2 Ceq definition of capacitance series sphere V ED R1 + R2 +… = Req series C1 +C2 +… = Ceq parallel uniform E-field PEAB qVAB definition of voltage Constants: KEAB PEAB KE 21 mv 2 q A V IR energy conservation o = 8.8 x 10-12 C2/Nm2 kinetic energy k = 9 x 109 Nm2/C2 charge density—plate e = 1.6 x 10-19 C elementary charge mp = 1.7 x 10-27 kg proton mass me = 9.1 x 10-31 kg electron mass Ohm’s law 1 Exam 3 Apr. 4, 2002 Physics 212 Spring 2002 Name________________________ 1) [25 points total] The circuit at right has been connected for a long time and has reached a steady state. There are no capacitors. Point A has no significance until part e. 15V R1 6 R3 a) [5 points] Find the total current through the battery. Show your reasoning. (neatly please:) R4 2 R2 3 1.5 R5 2 point A b) [5 points] Find the voltage across R3. Show your reasoning. c) [5 points] Find the current through R4. Show your reasoning. d) [5 points] Find the power dissipated by R6. Show your reasoning. e) [5 points] If the wire is cut at point A, what happens to the voltage across R3? Does it increase, decrease, or stay the same? You do not need a number for full credit. Show your reasoning (or show your work). 2 R6 2 Exam 3 Apr. 4, 2002 Physics 212 Spring 2002 Name________________________ 2) [25 points total] All questions below refer to the circuit at right. Use the junction rule and the loop rule, as well as the ideas of resistance in your reasoning. a) [5 points] How does the brightness of bulb A compare to the brightness of bulb E? Explain your reasoning. E A B D F C b) [5 points] How does the brightness of bulb A compare to the brightness of bulb D? Explain your reasoning. c) [5 points] How does the brightness of bulb D compare to the brightness of bulb E? Explain your reasoning. d) [5 points] How does the brightness of bulb D compare to the brightness of bulb F? Explain your reasoning. e) [5 points] How does the brightness of bulb A compare to the brightness of bulb F? Explain your reasoning. 3 G Exam 3 Apr. 4, 2002 Physics 212 Spring 2002 Name________________________ 3) [25 points total] The circuit at right has been connected for a long time and has reached a steady state. There are two capacitors. 15V a) [5 points] Find the total current through the battery. Show your reasoning. R1 6 C1 R4 10F R2 2 2 C2 R5 R3 30F 2 2 b) [5 points] Find the current through R4. Show your reasoning. c) [5 points] Find the voltage across C1 and the charge stored on C1. Show your reasoning. d) [5 points] Find the voltage across C2 and the charge stored on C2. Show your reasoning. e) [5 points] Now the charged capacitors are arranged as shown at right. Find the voltage across each capacitor after the system comes to equilibrium. Hint: The voltage across each will be the same and the total charge stored on both together cannot change. 4 C1 R4 10F R2 2 2 C2 30F Exam 3 Apr. 4, 2002 Physics 212 Spring 2002 Name________________________ 4) [25 points total] Two capacitors are arranged as in the class handout, except that they are of unequal capacitance. One is three times the capacitance of the other. Both arrangements are connected to a 12V battery. II I 10F 12V 10F 12V 30F 30F a) [5 points] What is the ratio of the charges on the capacitors in circuit I? Are they equal? 2:1? 3:1? 4:1? Show your reasoning. b) [5 points] What is the ratio of the charges on the capacitors in circuit II? Are they equal? 2:1? 3:1? 4:1? Show your reasoning. c) [7 points] Find the voltage across the 30F capacitor and the charge on the 30F capacitor in circuit II. Show your reasoning. d) [8 points] If circuit II is disconnected from the battery and the charged capacitors are connected to a resistor as shown, find the total charge that passes through the resistor and the total energy dissipated by the resistor as the system discharges. Show your reasoning. 5 10F 10 30F