Question

4. (to be graded) 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 10kW 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 (10 cm)2 parallel-plate capacitor with 1 mm plate separation and 100 V of 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 ~~ 0.5 m3 available 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?

Answer 1

Solution:

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