Why does the voltage of vinegar batteries in series not equal the sum of the individual voltages?

As well as demonstrating some basic electricity generation you will be demonstrating why we don't generate commercial electricity using NZ coinage and vinegar!

^{simulate this circuit – Schematic created using CircuitLab}

Figure 1. Every battery has an internal resistance which causes a voltage drop as current increases.

The effect of internal resistance is to cause voltage droop as current increases. A simple demonstration of this will be to hook up as shown with the multimeter set to mA when in the AM1 position (make sure you have the leads in the right sockets) and set to DC V in the VM1 position.

• Disconnect the LED. Measure the open-circuit voltage. There is no need to measure open-circuit current. It will be zero.
• Reconnect the LED. Measure the current and the voltage. Using this information you should be able to calculate the total internal resistance of your battery. \$R = \frac {V_{OC} - V_{LOADED}}{I} \$.

It's hard to say why you're not getting four times 0.96 V when connected in series but a photo may tell us more.

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Looking at the photo I suspect that you may have some leakage in your individual cells. If the sides of the washers or coins get wet there will be a partial short on the cell. To test this make four separate cells connected by wire rather than the stack.

When any battery is connected to a load its output voltage will drop a bit due to the internal resistance of the battery.

If you are constructing a battery then there are four simple things you can do to reduce the internal resistance of the battery:

1. Make the electrodes wider.

   • The resistance of the electrolyte is going to be inversely proportional to the cross section of electrolyte that the current travels through. Generally most of the current will travel in a straight line directly between the electrodes.
   • The rate at which the chemical reactions can occur is proportional to the area of the electrodes.
   • This is equivalent to wiring multiple batteries in parallel.

2. Reduce the spacing between the electrodes. The resistance of the electrolyte is going to be proportional to the distance that the current has to travel through it.

   • Using thinner cardboard, or using paper towels should reduce resistance.

3. Increase the concentration of ions in the electrolyte. The conductivity will be somewhat proportional to the concentration of ions.

   • For example, vinegar contains acetic acid. Using another brand of vinegar with a higher percentage of acetic acid could help.
   • If you use citric acid rather than vinegar, you can purchase pure citric acid powder from your local grocery store. It is usually in the baking isle.

4. Use an electrolyte that has higher ion mobility. The resistance of the electrolyte is going to be inversely proportional to the ion mobility.

   • Citric acid (found in lemon juice), and sodium bicarbonate (baking soda) both make good electrolytes.

In addition to internal resistance phenomenon which lowers the battery voltage under load, you should pay close attention to @Jasen comment about internal short circuits. Take a look at industrial-grade batteries, and you will notice that individual cells never share electrolyte.

I suggest you try to put a non-wettable film (like pieces of a plastic bag or candy wrap) between each coin from one cell and the washer from the next cell. Since you still need them to be connected electrically, put a small wire across your insulation layer. That should improve your battery output and bring the total voltage closer to the sum of voltages from individual cells, at least without load.