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# oldhw 12 - nguyen(jmn727 oldhomework 12 Turner(59070 This...

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nguyen (jmn727) – oldhomework 12 – Turner – (59070) 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points Four capacitors are connected as shown in the figure. 17 μ F 59 μ F 46 μ F 84 μ F 97 V a b c d Find the capacitance between points a and b . Correct answer: 126 . 848 μ F. Explanation: Let : C 1 = 17 μ F , C 2 = 46 μ F , C 3 = 59 μ F , C 4 = 84 μ F , and E = 97 V . C 1 C 3 C 2 C 4 E B a b c d A good rule of thumb is to eliminate junc- tions connected by zero capacitance. C 2 C 3 C 1 C 4 a b The definition of capacitance is C Q V . The series connection of C 2 and C 3 gives the equivalent capacitance C 23 = 1 1 C 2 + 1 C 3 = C 2 C 3 C 2 + C 3 = (46 μ F) (59 μ F) 46 μ F + 59 μ F = 25 . 8476 μ F . The total capacitance C ab between a and b can be obtained by calculating the capacitance in the parallel combination of the capacitors C 1 , C 4 , and C 23 ; i.e. , C ab = C 1 + C 4 + C 23 = 17 μ F + 84 μ F + 25 . 8476 μ F = 126 . 848 μ F . 002 (part 2 of 2) 10.0 points What is the charge on the 46 μ F upper- centered capacitor? Correct answer: 2507 . 22 μ C. Explanation: The voltages across C 2 and C 3 , respectively, (the voltage between a and b ) are V ab = V 23 = 97 V , and we have Q 23 = Q 3 = Q 2 = V ab C 23 = (97 V) (25 . 8476 μ F) = 2507 . 22 μ C . 003 (part 1 of 2) 10.0 points Consider a air-filled parallel-plate capacitor with plates of length 9 . 4 cm, width 6 . 19 cm, spaced a distance 1 . 15 cm apart. Now imagine that a dielectric slab with di- electric constant 3 . 4 is inserted a length 4 . 2 cm into the capacitor. The slab has the same width as the plates. The capacitor is com- pletely filled with dielectric material down to a length of 4 . 2 cm.

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nguyen (jmn727) – oldhomework 12 – Turner – (59070) 2 A battery is connected to the plates so that they are at a constant potential 0 . 17 V while the dielectric is inserted. 9 . 4 cm 4 . 2 cm 1 . 15 cm dielectric none - air bottom 1 . 0 dielectric constant top 3 . 4 What is the ratio of the new potential en- ergy to the potential energy before the inser- tion of the dielectric? Edge effects can be neglected. Correct answer: 2 . 07234. Explanation: Let : w = 6 . 19 cm , d = 1 . 15 cm , L = 9 . 4 cm , = 4 . 2 cm , κ = 3 . 4 , and V = 0 . 17 V .
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