2012年10月25日星期四
Could You Start Your Car With D-Cell Batteries?
I seem to recall a question like this in an introductory physics textbook. The basic idea was that your car has a 12-volt battery that is used to start the engine, right? Well, 8 D-Cell batteries in series will also make a 12-volt battery. However, not all 12-volt batteries are the same. The D-cells just won't do the job of starting your car.The problem is that as you increase the current out of a battery, the voltage across this battery does not stay constant but instead decreases. For example, take a D-cell and connect the negative and positive terminals with a plain copper wire. This wire has a ridiculously low resistance. Suppose the wire had a resistance of just 1 Ω, With a 1.5 volt potential difference, you would have 1.5 amps of current going through this wire. That's pretty high for a single D-cell battery.Then how can we model the actual voltage across a battery? The key is to model the battery as a constant change in potential along with a built in resistor in series with this. Here is my diagram of a D-cell battery.
This also shows why your D-cell won't start a car. Suppose you need 200 amps going to the starter motor for it to function correctly. Even if the internal resistance is just 1 Ω, that would be a 200-volt drop inside the battery. Of course, that is larger voltage drop than the internal battery itself. Bummer.There is a way to get 200 amps out of a D-cell – have a whole bunch of D-cells in parallel. Lets say I have 200 sets of 8 D-cells in parallel. In that case, each D-cell would only need to produce 1 amp of current. With them all together, this would be 200 amps.There are a couple of ways to determine the internal resistance of a battery. It is easy to determine the "internal" voltage. All you need to do is measure the voltage across the battery while it has no load (not connected to anything). Next, hook the battery up to some low (but known) resistance. Like this.Just a check. This does have the correct units. Also, if the battery has a really low internal resistance, the voltage across the battery will be about the same as the "internal" voltage. This is essentially what this equation says.The only thing is that to use this method, you need to know the resistance value of the load you put on the battery. There is another way.What if I measure the current and the voltage across the battery for a variety of resistance loads? In this, case, I would expect the following relationship.From this, I can plot the voltage across the battery as a function of the current coming out of the battery. This way I can put whatever resistors I like for a load and it just doesn't even matter what these values are. The nice thing about this other method is that it uses more data points and ignores the resistance. If I take a 10Ω resistor and hook it up to a battery, it might not actually be 10Ω. Resistors don't always have a constant resistance.
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