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*Question:* A capacitor of capacitance
is charged up to a
voltage of
, and then discharged by connecting a
resistor of resistance
across its terminals. How
long does it take for the charge on the positive plate of the capacitor to
be reduced to of its original value?

*Answer:* Suppose that the resistor is first connected across the
capacitor at . The charge on the positive plate of the capacitor
is given by

which can be rearranged to give

Taking the natural logarithm of both sides, we obtain

Hence,

where

is the time. Since , in this case, it follows that

** Next:** Example 10.5: The step-up
** Up:** Inductance
** Previous:** Example 10.3: The RL
Richard Fitzpatrick
2007-07-14