|MadSci Network: Physics|
Hi Sarah, That's an excellent question! Measuring internal resistance is a little more complicated. In general, the internal resistance of a battery is not a fixed value. It varies over time as the battery loses energy and also varies depending on the load, or how much current is drawn from the battery. Engineers refer to this as a non-linear resistance. You might also find that if really load down a battery, the internal resistance changes dramatically. In order to fully characterize the internal resistance, we need to take measurements over time and for different loads. The result is a set of graphs, each plotting values of resistance as a function of load current. This can be an involved process, depending on how much data you want. We can, however, get an estimate of the internal resistance by taking only two measurements with a voltmeter. First, we need to measure the "open circuit" voltage of the battery. This is simply the voltage at the battery terminals when no current is being drawn. Practically, it's hard to measure voltage without drawing some current, but most voltmeters have a high enough input resistance that it can be neglected. So we first measure the open circuit voltage, Vo. Let's say it's 0.9 volts, as in your case. Now we need to load down the battery and measure the voltage at the battery terminals again, let's call that Vl. Let's call the load resistance Rl. Given all those values, the equation for the internal resistance (Ri) of the battery is: Equ 1: Ri = Rl * ((Vo/Vl) - 1) You can derive this equation from the equation for a voltage divider: Equ 2: Vl = Vo * Rl / (Ri + Rl) This equation can be derived from application of Ohm law and Kirchoffs law. You can find that information from any text on electric circuit theory. Now we need to choose a value of Rl that gives us good numbers. From inspection of equ 2, we can observe that if Rl equals Ri, the load voltage will be exactly half of the open circuit voltage. This trick is commonly used if you have a variable resistor within the range of internal resistance. This is not always possible, so you might have to use several fixed resistors of different values. You will probably find that typical alkaline cells tend to have relatively low internal resistances when they are new. It's probably in the range of an ohm or so. You will probably need a resistor that is not more than 10 times that value to make good measurements. If you can find a 10 ohm resistor that's OK. Of course, you should start with higher values to see the effects. Start with 100 Ohms and see what you get. Then try lower values and run the calculations again. You can enter your values into a spreadsheet and plot the results. A word of caution: be careful when using low value resistors with good batteries, the current draw will be high enough the heat up the resistor (and the battery!). I hope that answers your question. Let me know what you find out!
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