An ultracapacitor is a very high-capacitance device capable of storing much more

Question

An ultracapacitor is a very high-capacitance device capable of storing much more energy than an ordinary capacitor. It is designed so that the spacing of the plates is around 1000 times smaller than in ordinary capacitors. Furthermore the plates contain millions of microscopic nanotubes, which increase their effective area 100,000 times. If the plate separation and effective area of a 30 mu F capacitor are changed as described above to make an ultracapacitor, what is its new capacitance How much energy does the ultracapacitor store if charged to 1.5 V Compare this to the energy in an orcMary 30 mu F capacitor at that potential. Compare the energy stored in the ultracapacitor to that AAA. battery, which contains 6750 J. If the ultracapacitor is to take 1.0 min to decrease to 1/e of its initial maximum charge, what resistance must it discharge through

Explanation / Answer

(b) Energy stored = 0.5 * C * V^2 = 0.5 * 3000 * 1.5^2 = 3375 J = 3.375 KJ

'Ratio of energies of capacitor to ultra capacitor is = Ratio of capacitences (since voltage is constant)

So ratio is 3000/ 30 * 10^-6 = 10 ^8 times or 1e8

(c) Energy stored by capacitor / battery = 3375 / 6750 = 0.5

(d) from discharge of capacitor Q = Q0 ( e -t/RC)

So

t/RC = 1 So 60 = R * 3000 So R = 20 milli ohms

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