Phys121-13sol

Phys121-13sol - Anderson Matthew Homework 13 Due noon Inst...

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Anderson, Matthew – Homework 13 – Due: Apr 29 2008, noon – Inst: Vitaly 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 3) 10 points An LC circuit is shown in the figure below. The 20 pF capacitor is initially charged by the 7 V battery when S is at position a . Then S is thrown to position b so that the capacitor is shorted across the 10 mH inductor. 10 mH 20 pF 7 V S b a What is the maximum value for the oscil- lating current assuming no resistance in the circuit? Correct answer: 0 . 00031305 A. Explanation: Let : C = 20 pF = 2 × 10 - 11 F , L = 10 mH = 0 . 01 H , and E = 7 V . The maximum charge on the capacitor is Q max = C V . The maximum current is I max = ω Q m = ω C V , where ω is the oscillatory frequency given by ω = 1 L C . Thus I max = r C L V = r 2 × 10 - 11 F 0 . 01 H (7 V) = 0 . 00031305 A . 002 (part 2 of 3) 10 points What is the natural angular frequency of the circuit? Correct answer: 2 . 23607 × 10 6 rad / s. Explanation: ω = 1 L C = 1 p (0 . 01 H) (2 × 10 - 11 F) = 2 . 23607 × 10 6 rad / s . 003 (part 3 of 3) 10 points What is the maximum energy stored in the magnetic field of the inductor? Correct answer: 4 . 9 × 10 - 10 J. Explanation: U max,ind = U max,cap = Q 2 max 2 C = 1 2 C V 2 .

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