This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: choe (dec865) Practice HW 18 Solutions Weathers (22202) 1 This printout should have 13 questions. Multiplechoice 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 s later the energy stored in the capacitor is onefourth its initial value. Find the inductance if the capacitance is 3 pF. Correct answer: 0 . 0273567 H. Explanation: Let : t = 0 . 3 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( t + ) , where = 1 L C . To determine the phase angle in the above equation, we use the initial condition that, at t = 0, the charge is maximum. Thus Q max = Q max cos 1 = cos = 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 onefourth 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 = 3 rad . Solving for L gives L = 9 t 2 2 C = 9 (3 10 7 s) 2 2 (3 10 12 F) = . 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 . choe (dec865) Practice HW 18 Solutions Weathers (22202) 2 Using the equation = 1 L C , the frequency is...
View
Full
Document
This document was uploaded on 09/23/2010.
 Spring '09
 Work

Click to edit the document details