chapter18.5-18_updated

chapter18.5-18_updated - 2/6/2009 When the switch is...

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2/6/2009 1 When the switch is closed, the capacitor starts to charge The capacitor continues to charge until it reaches its maximum charge (Q = C D V= C e ) Once the capacitor is fully charged, the current in the circuit is zero Demo The charge on the capacitor varies with time =RC is the time constant of the RC circuit (Need calculus to establish the above equation ) Q is the maximum charge e is the so-called Euler’s constant, the base of the natural logarithms e=2.718 28182845904523…. ) 1 ( ) ( / t e Q t q ) 1 ( ) ( / t e Q t q V C Q D
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2/6/2009 2 The time constant represents the time required for the charge to increase from zero to 63.2% of its maximum The greater C, the longer it takes The greater R, the slower the charging (the longer it takes) Demo: Large vs small RC ) 1 ( ) ( / t e Q t q RC ? Why RC Where does this 63.2% come from? ) 1 ( ) ( / t e Q t q ) 1 ( ) ( / t e Q t q RC Q e Q 632 . 0 ) 1 ( 1 368 . 0 1 e
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2/6/2009 3 The time constant of the circuit on the right is (1) (2) (3) (4) RC RC 5 25 When will the capacitor be charged to its maximum value? It takes …, well, forever…
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chapter18.5-18_updated - 2/6/2009 When the switch is...

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