Question

You’ve been hired by Elon Musk for a secret project within Tesla.Rather than annoying battery technology with its slow charging and limited lifetime, he wants to try to power cars by storing the energy in capacitors.

(a) If a small car with an efficient electric motor consumes about 10 kW of power on average, and we’d like to be able to drive for several hours before recharging ,about how much energy, in J, do we need to be able to store? (To check your estimate, a gallon of gasoline can be converted into about 108 J of useful energy– but cars are far from 100% efficient.)

(b) Start with a small (10cm)2parallel-plate capacitor with 1mm plate separation and 100 Vof potential. How much energy is stored?

(c) Hmmm. That won’t work. Estimate how much area you might be able to provide by connecting many such capacitors in parallel, while still fitting inside say∼0.5m3available space.

(d) We can also try increasing the voltage. However, at an electric field of 800 V/mm, air is ionized (this is called the “dielectric strength” of the dielectric that air is),so we can’t go above that without the capacitor shorting out. At this voltage and your higher area, how much energy can you store?

(e) By using a dielectric instead of air, you can do better. Two possibilities would be T iO2, with κ = 100 and a strength of 6 kV/mm, or Ruby Mica, with κ = 5.4 and a strength of 160 kV/mm. Which is better, and how much energy storage does this get you to?

(f) You see the challenge. (for some fun:) However, engineers are very clever, and as mentioned in the last problem set there are devices called ‘ultracapacitors’ that can do quite a bit better. Do some searching on the web to find

(a) the largest energy in 0.5 m3 that you can find, and

(b) some explanation as to how they store that much energy. Using these, what would you recommend in terms of electric vehicles?

Answer 1