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Practice Homework 18 2010

# Practice Homework 18 2010 - choe(dec865 – Practice HW 18...

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choe (dec865) – Practice HW 18 Solutions – Weathers – (22202) 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Initially, the capacitor in a series LC circuit is charged. A switch is closed, allowing the capacitor to discharge, and 0 . 3 μ s later the energy stored in the capacitor is one-fourth its initial value. Find the inductance if the capacitance is 3 pF. Correct answer: 0 . 0273567 H. Explanation: Let : t = 0 . 3 μ s = 3 × 10 7 s and C = 3 pF = 3 × 10 12 F . The capacitor charge in an oscillating LC circuit is Q ( t ) = Q max cos( ω t + φ ) , where ω = 1 L C . To determine the phase angle φ in the above equation, we use the initial condition that, at t = 0, the charge is maximum. Thus Q max = Q max cos φ 1 = cos φ φ = 0 rad . The energy stored in the capacitor at any given time is U ( t ) = 1 2 Q ( t ) 2 C . When the energy is one-fourth its initial value, we find that U ( t ) = 1 4 U (0) 1 2 Q ( t ) 2 C = 1 4 parenleftbigg Q 2 max 2 C parenrightbigg Q ( t ) = 1 2 Q max 1 2 = cos parenleftbigg t L C parenrightbigg t L C = cos 1 parenleftbigg 1 2 parenrightbigg = π 3 rad . Solving for L gives L = 9 t 2 π 2 C = 9 (3 × 10 7 s) 2 π 2 (3 × 10 12 F) = 0 . 0273567 H . 002 (part 1 of 3) 10.0 points An LC circuit is shown in the figure below. The 13 pF capacitor is initially charged by the 16 V battery when S is at position a . Then S is thrown to position b so that the capacitor is shorted across the 1 . 5 mH inductor. 1 . 5 mH 13 pF 16 V S b a Find the frequency of the oscillations. Correct answer: 1 . 13973 × 10 6 Hz. Explanation: L C E S b a Let : C = 13 pF = 1 . 3 × 10 11 F , L = 1 . 5 mH = 0 . 0015 H , and E = 16 V .

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choe (dec865) – Practice HW 18 Solutions – Weathers – (22202) 2 Using the equation ω = 1 L C , the frequency is f = ω 2 π = 1 2 π L C = 1 2 π
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Practice Homework 18 2010 - choe(dec865 – Practice HW 18...

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