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Phys 0175 - Lecture 19

# Phys 0175 - Lecture 19 - Lecture 19(Feb 25 2009 Chapter 27...

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Lecture 19 (Feb. 25, 2009): Chapter 27: Circuits (conclusion) R-C circuits – charging up a capacitor R-C circuits – discharging a capacitor Illustrative examples

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Resistance-Capacitance (RC) Circuits: How does the charge q on the capacitor vary with time after the switch is closed?
The instantaneous potential differences across R and C are: v ab = i*R and v bc = q/C The loop rule yields: E – i*R – q/C = 0 or i = E /R – q/RC i = 0 when E /R = q/RC or q = Q f = C* E

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Current i and charge q as functions of time when charging a capacitor C=1μF through a resistor R=2kΩ to a voltage E =10V: / / 0 t RC t RC dq i e I e dt R - - = = = E ( 29 ( 29 / / * 1 1 t RC t RC f q C e q e - - = - = - E time constant τ = RC = 2.0ms [RC has units of seconds]
When a charged capacitor is being discharged, i = dq/dt = - q/RC (no emf in loop)

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Current i and charge q as functions of time when discharging a capacitor: / / 0 0 t RC t RC q dq i e i e dt RC - - = = - = / 0 t RC q q e - =
If the RC circuit consists of more than one resistor and/or more than one capacitor, the time constant is determined by using R equ and C equ , the equivalent values of R and C for the circuit.

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Illustrative Example 19.1:
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Phys 0175 - Lecture 19 - Lecture 19(Feb 25 2009 Chapter 27...

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