Chapter 24

# Chapter 24 - Chapter 24 Capacitance Conceptual Problems 1...

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Chapter 24 Capacitance Conceptual Problems 1 If the voltage across a parallel-plate capacitor is doubled, its capacitance ( a ) doubles ( b ) drops by half ( c ) remains the same. Determine the Concept The capacitance of a parallel-plate capacitor is a function of the surface area of its plates, the separation of these plates, and the electrical properties of the matter between them. The capacitance is, therefore, independent of the voltage across the capacitor. ) ( c is correct. 2 If the charge on an isolated spherical conductor is doubled, its self- capacitance ( a ) doubles ( b ) drops by half ( c ) remains the same. Determine the Concept The capacitance of an isolated spherical capacitor is given by R C 0 4 π = , where R is its radius. The capacitance is, therefore, independent of the charge of the capacitor. ) ( c is correct. 3 True or false: The electrostatic energy density is uniformly distributed in the region between the conductors of a cylindrical capacitor. Determine the Concept False. The electrostatic energy density is not uniformly distributed because the magnitude of the electric field strength is not uniformly distributed, 4 If the distance between the plates of a charged and isolated parallel- plate capacitor is doubled, what is the ratio of the final stored energy to the initial stored energy? Determine the Concept The energy stored in the electric field of a parallel-plate capacitor is related to the potential difference across the capacitor by . 2 1 QV U = If Q is constant, U is directly proportional to V and doubling V doubles U . Hence the ratio of the initial stored energy to the final stored energy is 2 . 5 [SSM] A parallel-plate capacitor is connected to a battery. The space between the two plates is empty. If the separation between the capacitor plates is tripled while the capacitor remains connected to the battery, what is the ratio of the final stored energy to the initial stored energy? Determine the Concept The energy stored in a capacitor is given by QV U 2 1 = and the capacitance of a parallel-plate capacitor by . 0 d A C = We can 2287

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Chapter 24 2288 combine these relationships, using the definition of capacitance and the condition that the potential difference across the capacitor is constant, to express U as a function of d. Express the energy stored in the capacitor: QV U 2 1 = (1) Use the definition of capacitance to express the charge of the capacitor: CV Q = Express the capacitance of a parallel-plate capacitor in terms of the separation d of its plates: d A C 0 = where A is the area of one plate. Substituting for Q and C in equation (1) yields: d AV U 2 2 0 = Because d U 1 , tripling the separation of the plates will reduce the energy stored in the capacitor to one-third its previous value. Hence the ratio of the final stored energy to the initial stored energy is 3 / 1 .
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Chapter 24 - Chapter 24 Capacitance Conceptual Problems 1...

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