Compact \"ultracapacitors\" with capacitance values up to several thousand farad

Question

Compact "ultracapacitors" with capacitance values up to several thousand farads are now commercially available. One application for ultracapacitors is in providing power for electrical circuits when other sources (such as a battery) are turned off. To get an idea of how much charge can be stored in such a component, assume a 1500 Fultracapacitor is initially charged to 12.0 V by a battery and is then disconnected from the battery.

Part A

If charge is then drawn off the plates of this capacitor at a rate of 0.70 mC/s , say, to power the backup memory of some electrical gadget, how long (in days) will it take for the potential difference across this capacitor to drop to 9.0 V ?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

A)

charge on capacitor when V = 12 V

Qi = CV = 1500 x 12 = 18000 C

when V = 9 V

Qf = 1500 x 9 = 13500 C

change in charge = Qi - Qf = 4500 C

time = charge / rate

t = (4500 C ) / (0.70 x 10^-3 C /s) = 6428571.43 s

t( in min) = 107142.86 min = 1785.71 hr = 74.40 days

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