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q3s - Physics 2212 K Summer 2009 Quiz#3 Solutions...

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Physics 2212 K Quiz #3 Solutions Summer 2009 ² 0 Permittivity constant m p Mass of a proton μ 0 Permeability constant m e Mass of an electron e Fundamental charge c Speed of light K Coulomb constant g Acceleration due to gravity Unless otherwise directed, friction, drag, and gravity should be neglected, and all batteries and wires are ideal. Any integrals in free-response problems must be evaluated. I . (24 points) The circuit illustrated has an emf E , and six capacitors, each with capacitance C . What is the potential energy stored in the capacitor at the upper right, marked with an asterisk ( * )? Express your answer in terms of parameters defined in the problem, and phys- ical or mathematical constants. (Let the potential energy stored in an uncharged capacitor be zero.) . . . . . . . . . . . . . . . If the charge on or potential across the asterisked capacitor can be found, then the energy stored in it can be determined. The equivalent capacitance of the circuit should be calculated. The three capacitors circled in red are in series. Their equivalent capacitance is C red = 1 C + 1 C + 1 C - 1 = 3 C - 1 = C/ 3 Redrawing the circuit with that combination, one can see that the three capacitors circled in blue are in parallel. Their equivalent capacitance is C blue = C + C + C/ 3 = 7 C/ 3 Redrawing the circuit with that combination, one can see that the aster- isked capacitor is in series with all the rest. The equivalent capacitance of the circuit is C eq = 1 7 C/ 3 + 1 C - 1 = 3 7 C + 7 7 C - 1 = 10 7 C - 1 = 7 C/ 10 The charge delivered by the battery is Q = C eq Δ V = 7 C 10 E and since the asterisked capacitor is in series with all the rest, this must also be the charge on it. Therefore, the energy stored in the asterisked capacitor is U = Q 2 2 C = ( 7 C 10 E ) 2 2 C = 49 200 C E 2 Quiz #3 Solutions Page 1 of 4
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1. (6 points) An electric potential that depends only on
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