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worksheet12 Michigan State University PHY 102
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  • Title: worksheet12
  • Type: Notes
  • School: Michigan State University
  • Course: PHY 102
  • Term: Spring

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#12 Worksheet - PHY102 (Spr. 2006) DC and AC circuits Due Thursday April 13th 9pm In earlier worksheets we have studied the behavior of damped, massspring systems. We also took a brief look at the linear and non-linear pendulum problems. The equations describing these problems also describe the behavior of linear and non-linear circuits and there are many analogies between mechanical and electrical problems that are often used in the physics discussions. For example the concepts of underdamped, critically damped and overdamped apply to electrical problems as well as to mechanical problems. Similarly the concept of resonance applies to both mechanical and electrical problems. In circuits, a resistor absorbs energy and acts as the damping. In mechanical problems energy is transferred between potential energy and kinetic energy. In electrical problems energy is transferred between energy stored in the magnetic field and energy stored in the electrical field. In the case of circuits energy is transferred between capacitors and inductors. The relation between the magnitudes of the voltage and current in circuit elements L,R,C are as follows: dI 1 t , VC = Idt (1) dt C 0 Kirchhoff's voltage law states that the sum of the voltage drops around a series LRC circuit must sum to zero, yielding the following equation, VR = IR, VL = L Vs - V R - V L - V C = 0 (2) Using the relations between above the current and voltages for L,R,C given above we find, 1 t dI Idt = 0 (3) Vs - IR - L - dt C 0 Taking a derivative of this equation yields, d2 I I dI dVs -L 2 -R - =0 (4) dt dt dt C Recall that a damped mass-spring system is described by Fs - bv - kx = ma, so that, d2 x dx -Fs + m 2 + b + kx = 0 (5) dt dt 1 where Fs is the driving force on the mass-spring system. The analogies between the mass-spring system and the electric circuit are evident from these equations, that is, L acts like the mass, R like the damping and 1/C like the spring constant. The derivative of the source voltage acts like the driving force. Problems 1. (Transients) Consider a series LRC circuit connected to DC voltage of 1V. A switch in the circuit is initially open and the capacitor is initally uncharged. Consider closing the switch at time zero. Write a code to find and plot the current in the LRC circuit as a function of time. Run your code for values of L, R and C to illustrate the cases of underdamped and overdamped circuits. 2. (Resonance) Consider an LRC circuit driven by a steady sinusoidal AC source with amplitude 1V. Find and plot the amplitude of the steady state current in the circuit as a function of the ratio of the frequency of the AC source to the natural frequency of the LRC circuit. The natural frequency is given by, n = (1/LC - (R/2L)2 )1/2 (6) 2

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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
Description: Spring 2006 Thermodynamics Homework #12 Due Wednesday, 3/15/06 1. A 2 ft3 scuba diver\'s air tank is to be filled with air from a compressed air line at 120 psia, 100F. Initially, the air in the tanks is at 20 psia and 70F. Assuming that the tank is ...
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> CSE >> 860 Spring, 2004
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Path: Michigan State University >> CSE >> 860 Spring, 2004
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
Description: Spring 2006 Thermodynamics Homework #6 Solution 1. (10 pts) What is the enthalpy, internal energy, specific volume, and entropy for steam at 1107C and 27 MPa? Solution: Substance Type: Compressible (steam) Problem Type: State We are given steam at 2...
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> ME >> 201 Spring, 2006
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Path: Michigan State University >> PHY >> 410 Spring, 2007
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Path: Michigan State University >> PHY >> 410 Spring, 2007
Description: Physics 410 Homework 10: 1. 2. 3. 4. 5. 6. 7. (6 pts) (5 pts) (5 pts) (4 pts) (10 pts) (5 pts) (10 pts) Problem 5.54 Problem 6.10 Problem 6.14 Problem 6.18 Problem 6.22 Problem 6.28 Problem 6.30 from Schroeder. from Schroeder. from Schroeder. from Sc...
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Path: Michigan State University >> PHY >> 102 Spring, 2006
Description: # Worksheet 13 - 2006 Due Thursday 20th April 9pm This worksheet gives you some more practice at problem solving using mathematica. PROBLEM 1. Make a 3-d plot of the function Sin(xy) for x [0, 3] and y [0, 3]. PROBLEM 2. Numerically find the roots to...
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Path: Michigan State University >> PHY >> 102 Spring, 2006
Description: Worksheet #4 - PHY102 (Spr. 2006) Solving equations Solving equations in Mathematica Look up how to solve algebraic equations exactly(Solve) and numerically(NSolve). If you have a transcendental equation (e.b. x = sin(x) you need to use \"FindRoot\". I...
Physics 410 Homework 11
Path: Michigan State University >> PHY >> 410 Spring, 2007
Description: 1. (6 pts) Free energy of a two state system. (a) Find an expression for the free energy as a function of =kBT of a system with two states, one at energy 0 and one at energy . (b) From the free energy, find expressions for the energy and entropy of t...
Physics 410 Homework 9
Path: Michigan State University >> PHY >> 410 Spring, 2007
Description: Physics 410 Homework 9: 1. 2. 3. 4. 5. 6. (8 pts) (6 pts) (5 pts) (6pts) (4 pts) (5 pts) Problem 5.32 Problem 5.34 Problem 5.48 Problem 5.49 Problem 5.51 Problem 5.53 from Schroeder. from Schroeder. from Schroeder. from Schroeder. from Schroeder. fro...
Physics 410 Homework 13
Path: Michigan State University >> PHY >> 410 Spring, 2007
Description: Physics 410 Homework 13: 1. 2. 3. 4. 5. 5. (10 pts) (5 pts) (4 pts) (4 pts) (5 pts) (8 pts) Problem 7.28 Problem 7.31 Problem 7.37 Problem 7.39 Problem 7.45 Problem 7.46 from Schroeder. from Schroeder. from Schroeder. from Schroeder. from Schroeder. ...
Physics 410 Homework 6
Path: Michigan State University >> PHY >> 410 Spring, 2007
Description: Physics 410 Homework 6: 1. (10 pts) 2. (3 pts) 3. (12 pts) 4. (6 pts) 5. (4 pts) 6 . (7 pts) Problem 3.25 from Schroeder. Problem 3.33 from Schroeder. Problem 3.34 from Schroeder. Problem 3.37 from Schroeder. Problem 3.38 from Schroeder. Problem 3.39...
Physics 410 Homework 7
Path: Michigan State University >> PHY >> 410 Spring, 2007
Description: Physics 410 Homework 7: 1. (4 pts) 2. (8 pts) 3. (8 pts) 4. (4 pts) 5. (4 pts) 6 . (5 pts) 7 . (6 pts) 8 . (10 pts) Problem 4.4 Problem 4.6 Problem 4.14 Problem 4.17 Problem 4.19 Problem 4.20 Problem 4.30 Problem 4.33 from Schroeder. from Schroeder. ...
Physics 410 Homework 5
Path: Michigan State University >> PHY >> 410 Spring, 2007
Description: Physics 410 Homework 5: 1. (4 pts) Problem 3.1 from Schroeder. 2. (3 pts) Problem 3.4 from Schroeder. 3. (5 pts) Problem 3.8 from Schroeder. 4. (6 pts) Problem 3.10 from Schroeder. 5. (4 pts) Problem 3.14 from Schroeder. 6. (3 pts) Problem 3.19 from ...
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Path: Michigan State University >> LIR >> 832 Spring, 2007
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Path: Michigan State University >> PHY >> 321 Spring, 2006
Description: Physics 321 Spring 2006 Homework #7, Due at beginning of class Wednesday Mar 15. 1. [8 pts] A \"triangle wave\" can be defined by F (t) = 1 - 2|t|/ for -/ < t < +/, with F (t) defined at all other values of the time t by the property of having period ...
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Path: Michigan State University >> PHY >> 321 Spring, 2006
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Homework6
Path: Michigan State University >> PHY >> 321 Spring, 2006
Description: Physics 321 Spring 2006 Homework #6, Due at beginning of class Wednesday Mar 1. 1. [4 pts] A hook is at height y above the floor, where y is constant for all negative times: y = y0 for t < 0. For positive times, y oscillates: y = y0 + A sin t for t ...
2005final
Path: Michigan State University >> PHY >> 321 Spring, 2006
Description: PHYSICS 321 FINAL EXAM May 4, 2005 NAME 1. [5 pts] A particle of mass M moves in one dimension in the potential V (x) = a + bx where a and b are constants. Find all possible motions x(t). 2. [5 pts] The motion of a system with two degrees of freedom...
schedule_2007
Path: Michigan State University >> PHY >> 410 Spring, 2007
Description: Tentative Schedule: Week 1 2 3 4 5 6 7 8 Spring 9 10 11 12 13 14 15 Finals Month Jan Jan Jan Jan/Feb Feb Feb Feb Feb/Mar Break Mar Mar Mar/Apr Apr Apr Apr Apr April 22 29 5 12 19 26 5 12 19 26 2 9 16 23 30: M 8 W 10 17 24 31 7 14 21 28 7 14 21 28 4 1...
Physics 410 Homework 12
Path: Michigan State University >> PHY >> 410 Spring, 2007
Description: Physics 410 Homework 12: 1. 2. 3. 4. 5. (6 pts) (6 pts) (12 pts) (7 pts) (14 pts) Problem 7.2 Problem 7.6 Problem 7.8 Problem 7.16 Problem 7.23 from Schroeder. from Schroeder. from Schroeder. from Schroeder. from Schroeder. ...
Physics 410 Homework 2
Path: Michigan State University >> PHY >> 410 Spring, 2007
Description: Physics 410 Homework 2: 1. 2. 3. 4. 5. 6. 7. Problem 1.36 from Schroeder. Problem 1.40 from Schroeder. Problem 1.41 from Schroeder. Problem 1.44 from Schroeder. Problem 1.50from Schroeder. Problem 1.60 from Schroeder. Problem 1.63 from Schroeder. ...
Physics 410 Homework 4
Path: Michigan State University >> PHY >> 410 Spring, 2007
Description: Physics 410 Homework 4: 1. 2. 3. 4. 5. 6. (7 pts) Problem 2.30 from Schroeder. (4 pts) Problem 2.31 from Schroeder. (4 pts) Problem 2.32 from Schroeder. (4 pts) Problem 2.34 from Schroeder. (4 pts) Problem 2.37 from Schroeder. (6 pts) Problem 2.39 fr...
Physics 410 Homework 1
Path: Michigan State University >> PHY >> 410 Spring, 2007
Description: Physics 410 Homework 1: 1. 2. 3. 4. 5. 6. 7. Problem 1.8 from Schroeder. Problem 1.16 from Schroeder. Problem 1.21 from Schroeder. Problem 1.22 from Schroeder. Problem 1.25 from Schroeder. Problem 1.26 from Schroeder. Problem 1.33 from Schroeder. ...

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