a) A type of supercapacitor can withstand a maximum of 3.0 V across its plates.
ID: 3279563 • Letter: A
Question
a) A type of supercapacitor can withstand a maximum of 3.0 V across its plates. Show using a diagram how to combine a number of these capacitors so that current can be delivered at a maximum of 12 V. Find the capacitance of the combination if each capacitor is 3000 Farad. When fully charged at 12V the capacitor bank is required to deliver current at a minimum of 11V. Find out how much charge can be delivered by the capacitor bank as its voltage falls from the fully charged value of 12V to the minimum voltage of 11V. How long can a starter motor be operated from the capacitor if it draws a constant current of 100A? b) Now suppose that the dielectric medium of the capacitor has dielectric constant K 2000. Find out how much surface area of conductive plates is needed to make a 3000 Farad capacitor if the gap between conductors is 10 nanometres. c) What fraction of the total energy stored in the 3000F capacitor of b) is stored in the polarisation of the dielectric medium when it is charged to 3V? d) Suppose now that the dielectric in the capacitor of b)is a liquid. How much work is done by the charging device if the initially empty fully charged capacitor remains connected to the charger at 3V and then the capacitor is filled with its dielectric liquid. e) How much additional energy is stored in the capacitor at 3V when the liquid dielectric of d) is fully loaded, compared to the initial air filled condition? Is there a discrepancy with the amount of energy found in d)? Explain.Explanation / Answer
For part d.
capacitance of capacitor with dielectric Cd = 3000 F
capacitance of empty capacitor Ce = 3000/k F [ where k is dielectric constant of the dielectric]
k = 2000 given
so, for voltage source of V = 3 V
Energy stored in case 1, Ed = 0.5Cd*V^2 = 4.5*3000 = 13500 J
Energy stored in case 2, Ee = 0.5Ce*V^2 = 4.5*3000/2000 = 6.75 J
work done by battery = Ed - Ee = 13493.25 J
e. in this case again, the extra energy stored when dielectric is present is energy stored when dielectric is present - energy stored when dielectric is empty
dE = 13493.25 J,. this is exactly the same as the previous part
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.