p240_ct21_f07 - Physics 240 Fall 2007 Lecture #21 Dr. Dave...

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Physics 240 Fall 2007 Lecture #21 Dr. Dave Winn 2405 Randall Lab winn@umich.edu
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RC circuits In an RC circuit, energy stored as charge on a capacitor is dissipated in the resistor RC t E e Q Q C Q U = = 0 2 2 100 Ω 10 μ F 10 μ F In this circuit, the time constant RC is given by 100 Ω *10 μ F=10 -3 s
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RL circuits In RL circuits energy stored in the magnetic field of the inductor is dissipated in the resistor t L R B e I I Li U = = 0 2 2 1 I switch this to a and wait until current is flowing. Once the current is flowing, if I move the switch to b, it decays away. Time constant here is given by τ = L/R
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Inductors, resistors and capacitors Resistors have potential differences across them when currents flow through them : V = IR Inductors have potential differences across them when currents through them change : V = L(dI/dt) Capacitors have potential differences across them when there is charge on them : V = Q/C These three circuit elements describe the basic (linear) response of any circuit
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Energy storage in these two cases Energy is stored in the electric field in a capacitor when it is charged: U E = ½(Q 2 /C) Energy is stored in the magnetic field in an inductor when current flows through it: U B = ½Li 2 The energy density stored in electric field inside the capacitor is given by: u E = ε 0 E 2 /2 The energy density stored in the magnetic field of the inductor is given by: u B = B 2 /2 μ 0
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Oscillations Recall from Physics 140 that many systems with ‘restoring forces’ (negative feedback) will exhibit oscillations: 1. Mass on spring 2. Pendulum 3. Sloshing water In each case, energy is flowing back-and- forth between two different forms: 1. Kinetic and elastic potential (½mv 2 and ½kx 2 ) for mass on a spring 2. Kinetic and gravitational potential (½mv 2 and mgh) for a pendulum
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This note was uploaded on 04/04/2008 for the course PHYSICS 240 taught by Professor Davewinn during the Fall '08 term at University of Michigan.

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p240_ct21_f07 - Physics 240 Fall 2007 Lecture #21 Dr. Dave...

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