Phys 181b Problem Set 8 Solution

Phys 181b Problem Set 8 Solution - 1. (a) All the energy in...

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1. (a) All the energy in the circuit resides in the capacitor when it has its maximum charge. The current is then zero. If Q is the maximum charge on the capacitor, then the total energy is U Q C == × × 2 6 2 6 6 2 290 10 2360 10 117 10 . . . C F J. c h c h (b) When the capacitor is fully discharged, the current is a maximum and all the energy resides in the inductor. If I is the maximum current, then U = LI 2 /2 leads to I U L × × 2 21168 10 75 10 558 10 6 3 3 . . J H A. c h
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11. (a) Q = CV max = (1.0 × 10 –9 F)(3.0 V) = 3.0 × 10 –9 C. (b) From UL I Q C == 1 2 2 1 2 2 / we get I Q LC × ×× −− 30 10 10 10 17 10 9 39 3 . .. . C HF A. c hc h (c) When the current is at a maximum, the magnetic field is at maximum: I B ,max . × × = × 1 2 1 2 17 10 4 5 10 23 3 2 9 HA J . c hc h
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25. Since ω ' , we may write T = 2 π / as the period and = 1/ LC as the angular frequency. The time required for 50 cycles (with 3 significant figures understood) is () ( ) 36 2 50 50 50 2 50 2 220 10 H 12.0 10 F 0.5104s. tT L C −− π §· == = π = π × × ¨¸ ©¹ = The maximum charge on the capacitor decays according to qQ e Rt L max / = 2 (this is called the exponentially decaying amplitude in §31-5), where Q is the charge at time t = 0 (if we take φ = 0 in Eq. 31-25). Dividing by Q and taking the natural logarithm of both sides, we obtain ln q Q Rt L F H G
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This note was uploaded on 07/18/2008 for the course PHYS 181 taught by Professor Stephenirons during the Spring '08 term at Yale.

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Phys 181b Problem Set 8 Solution - 1. (a) All the energy in...

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