Electric Cars
In recent years, practical hybrid cars have hit the road - cars in which the gasoline engine runs a generator that charges batteries that run an electric motor. These cars offer increased efficiency, but significantly greater efficiency could be provided by a purely electric car run by batteries that you charge by plugging into an electric outlet in your house.
But there's a practical problem with such vehicles: the time necessary to recharge the batteries. If you refuel your car with gas at the pump, you add 130 of energy per gallon. If you add 20 gallons, you add a total of 2.6 in about 5 minutes. That's a lot of energy in a short time; the electric system of your house simply can't provide power at this rate.
There's another snag as well. Suppose there were electric filling stations that could provide very high currents to recharge your electric car. Conventional batteries can't recharge very quickly; it would still take longer for a recharge than to refill with gas.
One possible solution is to use capacitors instead of batteries to store energy. Capacitors can be charged much more quickly, and as an added benefit, they can provide energy at a much greater rate - allowing for peppier acceleration. Today's capacitors can't store enough energy to be practical, but future generations will.
Part A
A typical home's electric system can provide 100 at a voltage of 220 . If you had a charger that ran at this full power, approximately how long would it take to charge a battery with the equivalent of the energy in one gallon of gas?
Part B
The Tesla Roadster, a production electric car, has a 375 battery system that can provide a power of 200 . At this peak power, what is the current supplied by the batteries?
Part C
To charge the batteries in a Tesla Roadster, a transformer is used to step up the voltage of the household supply. If you step a 220 , 100 system up to 400 , what is the maximum current you can draw at this voltage?
Part D
One design challenge for a capacitor-powered electric car is that the voltage would change with time as the capacitors discharge. If the capacitors in a car were discharged to three quarters of their initial voltage, what fraction of energy would still be left?