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Unformatted text preview: Solution for Homework 10 Computing with Capacitance Solution to Homework Problem 10.1(What is Capacitance?) Problem: Capacitance is: Select One of the Following: (a) Work per unit charge. (b) Force per unit charge. (c-Answer) Charge per potential difference. (d) Force per unit field. Solution c: Charge per potential difference. Total Points for Problem: 2 Points Solution to Homework Problem 10.2(Decreasing Plate Separation of a Parallel-Plate Capacitor at a Constant Potential Difference ) Problem: A parallel-plate capacitor has a constant potential difference. While the potential difference across the capacitor remains unchanged, the separation between the plates is decreased. Which statement is true? Select One of the Following: (a) When the plate separation decreases, the charge amount on the capacitor plates increases. (b) When the plate separation decreases, the charge amount on the plates of the capacitor decreases. (c) Throughout the process, the charge amount on the capacitor plates remains unchanged. (d) When the plate separation decreases, the electric potential energy between the plates of the capacitor increases. (e-Answer) Both (a) and (d) are correct. Solution (a) Effect of Decreasing Plate Separation on Plate Charge Amount: The charge Q on a parallel-plate capacitor can be found using the relationship Q = C Δ V where Δ V is the potential difference between the plates of the capacitor and C is the capacitance. The potential difference between the plates of the capacitor is kept fixed. The capacitance of a parallel-plate capacitor is given by C = ε A/d . So, as plate separation decreases, the capacitance increases, and the charge increases. Option (a) is correct. (b) Effect of Decreasing Plate Separation on Energy Stored: The energy of a capacitor is given by U = 1 2 C (Δ V ) 2 . As the capacitance increases at fixed potential difference, the energy increases. Option (d) is also correct. Both options (a) and (d) are correct, so the correct answer is (e). Total Points for Problem: 3 Points Solution to Homework Problem 10.3(Energy in Coil Gun Capacitor) Problem: The capacitors in the coilgun at the website are 600 μ F with maximum voltage 800V . What is the maximum energy one of these capacitors can contain? Assume two significant figures. 1 Select One of the Following: (a) 96J (b-Answer) 190J (c) . 12J (d) . 24J (e) The answer is always (c), but I’m going to chose (e) anyway. Solution The energy stored in a capacitor is U = 1 2 C (Δ V ) 2 = 1 2 (600 × 10- 6 F)(800V) 2 = 190J Total Points for Problem: 3 Points Solution to Homework Problem 10.4(Energy of Charged Sphere as Radius is Changed) Problem: How does the energy of a uniformly charged spherical shell change as the radius of the sphere is increased without changing the total charge?...
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