241-29_Lec-18 - Physics 241 Lecture 18 Y. E. Kim October...

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Physics 241 Lecture 18 Y. E. Kim October 28, 2010 Chapter 29, Sections 8-10 October 28, 2010 University Physics, Chapter 26 and 27 1
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RC Circuits (from Chapter 26) RL Circuits Energy and Energy Density of a Magnetic Field Application to Information Technology October 28, 2010 Physics for Scientists & Engineers 2, Chapter 26 2
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October 28, 2010 University Physics, Chapter 26 3 RC Circuits (from Chapter 26) Consider a circuit with a source of emf, V emf , a resistor R, and a capacitor C We then close the switch, and current begins to flow in the circuit, charging the capacitor The current is provided by the source of emf, which maintains a constant voltage When the capacitor is fully charged, no more current flows in the circuit When the capacitor is fully charged, the voltage across the plates will be equal to the voltage provided by the source of emf and the total charge q tot on the capacitor will be q tot = CV emf
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October 28, 2010 University Physics, Chapter 26 4 Capacitor Charging (1) Going around the circuit in a counterclockwise direction we can write We can rewrite this equation remembering that i = dq / dt The solution of this differential equation is … where q 0 = CV emf and = RC 0 emf R C emf q V V V V iR C emf emf V dq q dq q RV dt C dt RC R 0 ( ) 1 t q t q e     The term V c is negative since the top plate of the capacitor is connected to the positive - higher potential - terminal of the battery. Thus analyzing counter-clockwise leads to a drop in voltage across the capacitor!
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October 28, 2010 University Physics, Chapter 26 5 Capacitor Charging (2) We can get the current flowing in the circuit by differentiating the charge with respect to time The charge and current as a function of time are shown here ( = RC ) t emf RC V dq ie dt R     0 ( ) 1 t q t q e  Math Reminder:
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October 28, 2010 University Physics, Chapter 26 6 Now let’s take a resistor R and a fully charged capacitor C with charge q 0 and connect them together by moving the switch from position 1 to position 2 In this case, current will flow in the circuit until the capacitor is completely discharged While the capacitor is discharging we can
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241-29_Lec-18 - Physics 241 Lecture 18 Y. E. Kim October...

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