9:46 & M A •4_591137447545825...ad cz1 c Jouandna id cuo m Iu:Ciouna Aof 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 areconnected at one end by a conducting wire. Find the capacitance per unit length of thissystem.25. A rectangular parallel-plate capacitor of length a and width b has a dielectric of width bpartially inserted a distance x between the plates, as shown in Figure . (a) Find thecapacitance as a function of x. Neglect edge effects. (b) Show that your answer gives theexpected results for x = 0 and x = a26. The two capacitors shown in Figure have capacitances C1 = 0.4 µ and C2 = 1 .2 µF. Thevoltages across the two capacitors are V1 and V2, respectively, and the total stored energyin the two capacitors is 1.14 mJ. If terminals band c are connected together, the voltage is4ADAMA SCIENCE AND TECHNOLOGY UNIVERSITY2020Va - Vd = 80 V; if terminal a is connected to terminal b, and terminal c is connected toterminal d, the voltage Va - Vd = 20 V Find the initial voltages V1 and V2d27. Two spheres have radii a and b, and their centers are a distance d apart. Show that thecapacitance of this system is4πεοC =112abdprovided d is large compared with a and b. Suggestion: Because the spheres are farassume 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 sphericalcapacitors in series28. Calculate the equivalent capacitance between points a and b in Figure P26.77. Notice thatthis system is not a simple series or parallel combination. Suggestion: Assume a potentialdifference AV between points a and b. Write expressions for AV in terms of the chargesand capacitances for the various possible pathways from a to b and require conservationаpart,of charge for those capacitor plates that are connected to each other.a4.00 µF2.00 μF 18.00 μF |T4.00 µF2.00 μF29. A parallel-plate capacitor in air has a plate separation of 1.50 cm and a plate area of 25.0cm2. The plates are charged to a potential difference of 250 V and disconnected from thesource. The capacitor is then immersed in distilled water. Assume the liquid is aninsulator. Determine (a) the charge on the plates before and after immersion, (b) thecapacitance and potential difference after immersion, and (c) the change in energy of theсараcitor.

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