7 - Version 035 Midterm2 li(59050 This print-out should...

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Version 035 – Midterm2 – li – (59050) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points The current in a circuit is tripled by connect- ing a 717 Ω resistor parallel with the resis- tance of the circuit. Determine the resistance of the circuit in the absence of the 717 Ω resistor. 1. 824.0 2. 1252.0 3. 920.0 4. 682.0 5. 1074.0 6. 510.0 7. 1364.0 8. 590.0 9. 766.0 10. 1434.0 Correct answer: 1434 Ω. Explanation: Let : R 1 = 717 Ω . If the initial resistance is R and the added resistance is R 1 we have 3 R = 1 R + 1 R 1 2 R = 1 R 1 R = 2 R 1 = 2(717 Ω) = 1434 Ω . 002 10.0 points Which of the following capacitors, each of which has plates of area A , would store the most charge on the top plate for a given po- tential difference V ? 1. V d Glass 2. V d/ 2 Air 3. V d/ 2 Vacuum 4. V d Vacuum 5. V d/ 2 Glass correct Explanation: The problem actually asks which capacitor has the largest capacitance, since, Q = C V . The capacitance for the parallel plate capaci- tor is C = κ ǫ o A d , so the largest κ and small- est distance gives the largest capacitance. Glass, being a dielectric material, has κ > 1, where the dielectric constant of air is 1. Therefore, the capacitor with the plate dis- tance d 2 and glass between plates has highest capacitance. 003 10.0 points Consider the capacitor circuit
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Version 035 – Midterm2 – li – (59050) 2 E B 9 μ F 2 μ F 8 μ F 3 μ F b a c Calculate the equivalent capacitance C ab between points a and b . 1. 3.42857 2. 4.73684 3. 4.44444 4. 3.75 5. 4.8 6. 5.5 7. 5.14286 8. 4.5 9. 4.63158 10. 5.0 Correct answer: 5 . 5 μ F. Explanation: Let : C 1 = 9 μ F , C 2 = 8 μ F , C 3 = 2 μ F , and C 4 = 3 μ F . E B C 1 C 3 C 2 C 4 b a c For capacitors in series, 1 C series = summationdisplay 1 C i V series = summationdisplay V i , and the individual charges are the same. For parallel capacitors, C parallel = summationdisplay C i Q parallel = summationdisplay Q i , and the individual voltages are the same. Let c be the point between the two parallel sections. Let c be the point between the two parallel sections. The capacitance between a an c is C l = C 1 + C 3 = 9 μ F + 2 μ F = 11 μ F . The capacitance between b and c is C r = C 2 + C 4 = 8 μ F + 3 μ F = 11 μ F . Thus the capacitance between a and b is 1 C ab = 1 C l + 1 C r = C r + C l C l C r C ab = C l C r C l + C r = (11 μ F) (11 μ F) 11 μ F + 11 μ F = 5 . 5 μ F . 004 10.0 points 3 . 6 Ω 2 . 6 Ω 12 . 4 Ω 15 . 6 V 7 . 8 V Find the current through the 12 . 4 Ω lower- right resistor. 1. 0.836735 2. 1.32632 3. 0.875912 4. 1.30088 5. 1.24419
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Version 035 – Midterm2 – li – (59050) 3 6. 1.0292 7. 1.36047 8. 0.481707 9. 0.784 10. 0.795918 Correct answer: 0 . 795918 A. Explanation: r 1 r 2 R E 1 E 2 A D E B C F i 1 i 2 I Let : E 1 = 15 . 6 V , E 2 = 7 . 8 V , r 1 = 3 . 6 Ω , r 2 = 2 . 6 Ω , and R = 12 . 4 Ω .
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