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Three concentric, thin conducting cylindrical shells have radii of 0.2, 0.5, and 0.8 cm. The space between the shells is filled with air. The innermost and outermost cylinders are connected at one end by a conducting wire. Find the capacitance per unit length of this system. A rectangular parallel-plate capacitor of length a and width b has a dielectric of width b

Three concentric, thin conducting cylindrical shells have radii of 0.2, 0.5, and 0.8 cm. The space between the shells is filled with air. The innermost and outermost cylinders are connected at one end by a conducting wire. Find the capacitance per unit length of this system. A rectangular parallel-plate capacitor of length a and width b has a dielectric of width b

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9:46 & M A • 4_591137447545825... ad cz1 c Jouandna id cuo m Iu:Ciouna A of charge on its plates, what is the unknown capacitance? 24. Three concentric, thin conducting cylindrical shells have radii of 0.2, 0.5, and 0.8 cm. The space between the shells is filled with air. The innermost and outermost cylinders are connected at one end by a conducting wire. Find the capacitance per unit length of this system. 25. A rectangular parallel-plate capacitor of length a and width b has a dielectric of width b partially inserted a distance x between the plates, as shown in Figure . (a) Find the capacitance as a function of x. Neglect edge effects. (b) Show that your answer gives the expected results for x = 0 and x = a 26. The two capacitors shown in Figure have capacitances C1 = 0.4 µ and C2 = 1 .2 µF. The voltages across the two capacitors are V1 and V2, respectively, and the total stored energy in the two capacitors is 1.14 mJ. If terminals band c are connected together, the voltage is 4 ADAMA SCIENCE AND TECHNOLOGY UNIVERSITY 2020 Va - Vd = 80 V; if terminal a is connected to terminal b, and terminal c is connected to terminal d, the voltage Va - Vd = 20 V Find the initial voltages V1 and V2 d 27. Two spheres have radii a and b, and their centers are a distance d apart. Show that the capacitance of this system is 4πεο C = 1 1 2 a b d provided d is large compared with a and b. Suggestion: Because the spheres are far assume the potential of each equals the sum of the potentials due to each sphere. (b) Show that as d approaches infinity, the above result reduces to that of two spherical capacitors in series 28. Calculate the equivalent capacitance between points a and b in Figure P26.77. Notice that this system is not a simple series or parallel combination. Suggestion: Assume a potential difference AV between points a and b. Write expressions for AV in terms of the charges and capacitances for the various possible pathways from a to b and require conservation аpart, of charge for those capacitor plates that are connected to each other. a 4.00 µF 2.00 μF 18.00 μF | T4.00 µF 2.00 μF 29. A parallel-plate capacitor in air has a plate separation of 1.50 cm and a plate area of 25.0 cm2. The plates are charged to a potential difference of 250 V and disconnected from the source. The capacitor is then immersed in distilled water. Assume the liquid is an insulator. Determine (a) the charge on the plates before and after immersion, (b) the capacitance and potential difference after immersion, and (c) the change in energy of the сараcitor.
Transcribed Image Text:9:46 & M A • 4_591137447545825... ad cz1 c Jouandna id cuo m Iu:Ciouna A of charge on its plates, what is the unknown capacitance? 24. Three concentric, thin conducting cylindrical shells have radii of 0.2, 0.5, and 0.8 cm. The space between the shells is filled with air. The innermost and outermost cylinders are connected at one end by a conducting wire. Find the capacitance per unit length of this system. 25. A rectangular parallel-plate capacitor of length a and width b has a dielectric of width b partially inserted a distance x between the plates, as shown in Figure . (a) Find the capacitance as a function of x. Neglect edge effects. (b) Show that your answer gives the expected results for x = 0 and x = a 26. The two capacitors shown in Figure have capacitances C1 = 0.4 µ and C2 = 1 .2 µF. The voltages across the two capacitors are V1 and V2, respectively, and the total stored energy in the two capacitors is 1.14 mJ. If terminals band c are connected together, the voltage is 4 ADAMA SCIENCE AND TECHNOLOGY UNIVERSITY 2020 Va - Vd = 80 V; if terminal a is connected to terminal b, and terminal c is connected to terminal d, the voltage Va - Vd = 20 V Find the initial voltages V1 and V2 d 27. Two spheres have radii a and b, and their centers are a distance d apart. Show that the capacitance of this system is 4πεο C = 1 1 2 a b d provided d is large compared with a and b. Suggestion: Because the spheres are far assume the potential of each equals the sum of the potentials due to each sphere. (b) Show that as d approaches infinity, the above result reduces to that of two spherical capacitors in series 28. Calculate the equivalent capacitance between points a and b in Figure P26.77. Notice that this system is not a simple series or parallel combination. Suggestion: Assume a potential difference AV between points a and b. Write expressions for AV in terms of the charges and capacitances for the various possible pathways from a to b and require conservation аpart, of charge for those capacitor plates that are connected to each other. a 4.00 µF 2.00 μF 18.00 μF | T4.00 µF 2.00 μF 29. A parallel-plate capacitor in air has a plate separation of 1.50 cm and a plate area of 25.0 cm2. The plates are charged to a potential difference of 250 V and disconnected from the source. The capacitor is then immersed in distilled water. Assume the liquid is an insulator. Determine (a) the charge on the plates before and after immersion, (b) the capacitance and potential difference after immersion, and (c) the change in energy of the сараcitor.
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