zhang18-3

# zhang18-3 - How is a capacitor charged and discharged When...

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2/2/2010 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 How is a capacitor charged and discharged? 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…. - is called the RC (time) constant ) 1 ( ) ( / t e Q t q ) 1 ( ) ( / t e Q t q V C Q D RC

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2/2/2010 2 The time constant represents the time required for the charge to increase from zero to 63.2% of its maximum The greater the C is, the longer it takes The greater the R is, 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
2/2/2010 3 When will the capacitor be charged to its maximum value? It takes …, well, forever…

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zhang18-3 - How is a capacitor charged and discharged When...

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