Capacitors won\'t hold a charge indefinitely; as time goes on, charge gradually

Question

Capacitors won't hold a charge indefinitely; as time goes on, charge gradually migrates from the positive to the negative plate. We can model this as a discharge of the capacitor through an internal "leakage resistance." A 0.50 F capacitor charged to 2.8 V will initially discharge with a leakage current of 0.30 mA. What is the leakage resistance? Express your answer to two significant figures and include the appropriate units. How long will it take for the capacitor voltage to drop to 1.0 V? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Part A)   leakage resistance =   2.8*103 / 0.30

                                               =   9333.33 ohm

Part B)    time taken

     =>    1 = 2.8 * e(-t/4666.66)

      =>   ln 0.3571 =    (-t/4666.66)

       =>   t =   4804.88 sec

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