Strange error in lemon battery experiment

Thread Starter

yovanov

Joined Mar 9, 2023
1
So my kids and I were trying to do the lemon battery experiment. Please read through as this is not the usual suspect mistake.

What happens is that we are getting very low readings from individual lemons (0.1-0.2V), but weirdly enough when we try making a series circuit, the voltage does not add up. It even drops sometimes. And yes, I am doing things right: zinc plated nails and copper, zink to copper connection, using aligator clip wires etc. I checked my voltmeter with regular 1.5 V batteries and it works fine. I am not even worried about powering a low voltage LED, I don't know why the series circuit does not add up voltage (looked up quite a bit on possible errors,, but every forum starts with "check to make sure you wire correctly, or you don't have enough amp to light a bulb, but see above, I'd like to know what could cause the series to not work).

I talked to a coleague professor from my university in the physics department (I am in math) and he tried to explain that if the internal resistence of the lemon is very high, then the voltmeter might yield errors (although even him admitted this is a bit difficult to imagine). I am just at a loss; I tried two types of lemons, also limes, two types of zinc nails. The series won't work. Even if I try one lemon with one usual 1.5 V battery they won't add up but rather give some strange reading of 0.9~1.1V, as if the lemon is more of a consumer. And no, I am not shorting inside the lemon (tried, it obviously reduces the reading to 0).

If anyone has any good technical idea of what could be going on, or heard of this before (beyond check the connections, reset and try again...) it would be very much appreciated. It has been frustrating also for the kids to watch all these online videos where this seems so easy, but when we try, not as much... :)

Thanks,
Mio
 

MrChips

Joined Oct 2, 2009
30,706
Welcome to AAC!

The answer provided by the physics professor is correct.

Every voltmeter will take current from the lemon battery. How much current it takes is important.
You can use basic Ohm's Law to calculate current.

Ohm's Law is written mathematically as,
I = V / R

where,
I = current in amps
V= applied voltage in volts
R = resistance of the load in ohms

Your voltmeter is the load and it has resistance. You can check the User Manual of your meter to find the resistance of the voltmeter. Or you can post the make and model of the meter and we will look it up for you.

A common value for many digital multimeters is 10MΩ.

Hence, when testing a 1.5V battery, the voltmeter is drawing 1.5V/10MΩ = 0.15μA

Here comes the problem.
Every battery also has resistance. We call this internal resistance of the battery. So now we have to factor in this resistance into the equation.

1678420570507.png

RL represents the 10MΩ resistance of the voltmeter.
Rs represents the internal resistance of the battery.

If Rs is of the same order of magnitude as RL you can see that we are not measuring the true battery voltage. The error gets worse when you put two lemon batteries in series. Thus, the problem is a mathematical one because we have failed to include two pieces of information, the internal resistance of the battery and the resistance of the voltmeter.

I will leave it up to you to do the math.

Don't be alarmed. This is a common phenomenon that we demonstrate in the first laboratory exercise in 2nd year Physics Electricity & Magnetism course at university.
 

MrChips

Joined Oct 2, 2009
30,706
After you have had a chance to think this over, see if you can devise an experiment to determine the internal resistance of the lemon battery and the true battery voltage.

It is easier than you think.

As a mathematician, you know that you need two equations to solve for two unknowns.
 

KeithWalker

Joined Jul 10, 2017
3,063
If anyone has any good technical idea of what could be going on, or heard of this before (beyond check the connections, reset and try again...) it would be very much appreciated. It has been frustrating also for the kids to watch all these online videos where this seems so easy, but when we try, not as much... :)

Thanks,
Mio
I think someone sold you a lemon! ;)
 

Ian0

Joined Aug 7, 2020
9,667
Do you know anyone in the chemistry department? If so, get a small quantity of citric acid and make up a solution in a beaker.
If that gives the right answer, then @KeithWalker is correct!
 

StefanZe

Joined Nov 6, 2019
191
Hi
Did you squeeze the lemon as much as possibly to break up the fluid-filled cells within the lemon?
If you don't do that before using it, the internal resistance will be very high, because the current hast to flow through the cell walls.
 
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