Virtual Science Ltd
The internal resistance of a dry cell
Introduction
This experiment allows you to measure the internal resistance of a single dry cell using a rheostat, a voltmeter, and an ammeter. The idea of a battery having a resistance can seem counterintuitive; surely the battery is the opposite of a resistor as it is creating a current, not resisting one? However, this is not correct. The chemical processes in a battery create the movement of electrons but these still have to overcome the resistance, no matter how small, of the battery itself. If it helps, think of the battery as something that incorporates a resistor; then, you can treat this resistor exactly as you would any other resistor in the circuit.
The objective
To find the internal resistance of a dry cell by plotting the relationship between the current and the voltage for a range of rheostat settings.
The apparatus
• A DC rheosta
• Two multimeters
• A single dry cell battery and battery box
• Some electrical wire
The device on the left of the picture is a rheostat, which is basically a variable resistor that can handle reasonably large currents. The rheostat consists of a large coil of wire. Note that there are three connection points: A and C are at each end of the coil, and B is connected by the top metal bar to the sliding connector shown at the middle of the coil. We only need the rheostat connected at A and B to create our variable resistance. When the slider is at the far right, the rheostat is set to its maximum resistance, as the electricity must go through all the windings of the coil. When the slider is at the left, the rheostat is set to its minimum resistance, as the electricity does not have to go through any of the windings of the coil. You should be careful not to move the slider all the way to the left, as this would cause a short circuit.
The Circuit
A dry cell is connected in series with a rheostat and an ammeter. A voltmeter is connected across the dry cell (which is also effectively across the rheostat, as the ammeter has negligible resistance).
The variables
The independent variable is the current that you are controlling with the rheostat. The dependent variable is the voltage
The Physics
The energy generated per second within the battery equals the energy transferred into the circuit and into the internal resistance of the battery. Effectively this energy warms the coil of the rheostat and the battery itself, which is why batteries get hot when used (especially high-drain batteries, such as those used in radio-controlled models, which get very hot indeed).
ɛI = I^2R + I^2r
Where ɛ is the electromotive force of the battery, I is the current, R is the resistance of the rheostat, and r is the internal resistance of the cell. Divide both sides through by I to get:
ɛ = IR + Ir
Now rearrange to get:
IR = ɛ – Ir
This is the equation of a straight line with intercept ɛ and gradient –r. Hence, the gradient of your graph gives you the internal resistance of the cell.
The method
Once you have constructed the circuit, set the rheostat to its max resistance by moving the slider as far as you can to the right.
Close the switch and take readings of voltage V and current I, then open the switch.
Adjust the rheostat to obtain a wide a range of pairs of readings for V and I.
Open the switch between readings (to prevent the battery becoming discharged).
The Video
Watch a video of the Internal Resistance e-practical here.
This shows how to use it and how to collect the data.
The E-Practical
Perform the experiment yourself, collect your own data, make mistakes and be able to correct them. The e-practical requires that your browser can run WebGL 2 (usually found on Windows browsers, safari on iOS, and various Mobile browsers, test with https://get.webgl.org/webgl2/). This link is for students and evaluation only, schools should purchase a site licence.
The first thing you need to do is connect the components together. To do this, you need to click on the start point and end point of each connection in sequence. When you click on where both ends of a wire are connected, the connecting wire will appear. Once all the wires are in place, the circuit will work, and the experiment can begin.
You can move the central contact of the rheostat by positioning the mouse cursor over the middle contact and using the mouse wheel (or dragging if using onscreen controls). In the e-practical, you cannot move the slider all the way to the left, to prevent the battery short-circuiting.
The Results
Plot a graph of V against I with V on the Y-axis. The gradient is the internal resistance.
Further Discussion
Were you surprised at how low the internal resistance is? Can you calculate how much energy (as a percentage) is wasted on heating the battery?
Lithium polymer (LiPo) batteries, used in model cars and planes, get extremely hot while in use. Explain this. Do they have higher-than-normal internal resistance, or is this due to something else?
This section is adapted from material developed by Dr Robert Lucas and is related to the book High School and Undergraduate Physics Practicals, published by CRC Press.