B Troubleshooting Battery Internal Resistance Measurements

[sophiecentaur]

The purpose of the experiment I am doing has not changed at all.

OK that's all fine and you are clearly getting somewhere useful. It was only the 'aside' that I didn't understand.
My question still remains about what that graph in post #89 is all about. What 'component' do the values of Conductance represent? Are they the load conductance? What did you measure that with? Did you actually need to - if V across the cell and I are all that's used?

Also, people (not just me) really appreciate proper schematic diagrams for describing electrical experiments. Photos are a bit like verbal versions of equations in that they're open to misinterpretation. For simple circuits they are very easy to produce with an object based drawing app (not shakey-hand-drawn as in Paint). PowerPoint and other similar apps are available for most people. Even Excel has the basic Microsoft system for building items from shapes. Once learned, never forgotten.

 

[neilparker62]

OK that's all fine and you are clearly getting somewhere useful. It was only the 'aside' that I didn't understand.
My question still remains about what that graph in post #89 is all about. What 'component' do the values of Conductance represent? Are they the load conductance? What did you measure that with? Did you actually need to - if V across the cell and I are all that's used?

Also, people (not just me) really appreciate proper schematic diagrams for describing electrical experiments. Photos are a bit like verbal versions of equations in that they're open to misinterpretation. For simple circuits they are very easy to produce with an object based drawing app (not shakey-hand-drawn as in Paint). PowerPoint and other similar apps are available for most people. Even Excel has the basic Microsoft system for building items from shapes. Once learned, never forgotten.

Concerning the graph in post #89.

I derived the following equation: $$I \approx E_{cell} \times G - E_{cell} \times r_i G^2 $$. This equation is of the form $y=ax + bx^2$ with y=I and x=G. Quadratic regression on the x,y pairs will yield the coefficients a $=E_{cell}\;$ the cell emf and b $=-E_{cell} \times r_i$. "b" can be divided by the already obtained value of "a" to determine $r_i$ the internal resistance of the cell.

In this equation G is indeed the load conductance - the reciprocal of load resistance R. It is obtained from the measured load volts and amps simply by dividing measured load amps by measured load volts.

The graph in post #89 looks very linear and indeed it is because the above quadratic expression is dominated by the term $E_{cell} \times G$ which would represent ideal battery behaviour in the case $r_i=0$. Remarkably however the quadratic regression fit does yield quite convincing values for both cell emf and internal resistance. A parabola can look very linear over certain limited domains.

Concerning circuit schematic

Please see following summary of the experimental procedure for the "A level" physics prac. The circuit diagram does not show it but they do mention including a second resistor to limit current. In my case the pencil showing in my photo acted as that second resistor providing a minimum load of about $13\;\Omega$. Perhaps $15 \Omega$ would be better since we need to limit current draw to values that do not significantly alter cell emf (open circuit voltage) over the course of the experiment. The rheostat shown in the circuit diagram is my exposed pencil lead which enables one to change load resistance/conductance simply by changing the point of attachment of the crocodile clip.

In the circuit diagram referred to above, there are misleading 'wires' apparently connecting battery terminals to voltmeter leads. There should be no such 'parasitic' resistance between battery terminals and voltmeter leads - that is the exact point of Dave's 4-wire measurement setup (if I understand it correctly ?).

 

[neilparker62]

So here's my setup to measure internal resistance using battery test mode on my multimeter. The meter's manual indicates that when testing a 1.5V battery, current draw will be about 50 milli amps. From which I infer that the "battery test" setting is supplying the battery under test with a 30 ohm load as per circuit diagram above. If there was no lead resistance we could directly determine the battery's internal resistance from $$r_i=\frac{\Delta V}{I}$$ where $\Delta V=E_{cell}-V_1$ and $I=\frac{V_1}{30}$.

If both meters above are set to read open circuit volts, then the readings will be the same since there will be no 30 ohm resistor and no current in the circuit. However if the meter measuring $V_1$ is now set to "battery test" , the 30 ohm resistor is connected and current flows. There is now a small terminal voltage drop for both $V_1$ and $V_2$ but $V_1$ drops marginally more - by measurement this difference is 7 or 8 millivolts. The difference is due to lead resistance and can be divided by load current to obtain a value for lead resistance. Given $I_{load} \approx 50 mA$ we can determine lead resistance as $\approx \frac {7.5}{50}=0.15 \Omega$.

Having determined lead resistance, we may now dispense with $V_2$ and move back to the simple method described in paragraph 1 above. And just subtract $0.15 \Omega$ from the calculated $r_i$ value obtained accordingly. Here are some results I have obtained using this technique. The dataset is ordered on the last column. Voltage readings are in milli volts.

 

[neilparker62]

Data below is for Energiser Rechargeables with $r_i$ between 30 and 40 milli-ohms. We obtain about 33 milli ohms. A bit different using regression statistics - 37 milli ohms based on $\frac{V_L}{E}\approx 1- r_i G.$ Exceptional AA batteries - they hardly 'bend' at all when drawing currents between 200 and 400 milli-amps.

 

[neilparker62]

I've written an Insights article on the above and quoted or linked to a number of contributing posts - I hope the relevant contributors won't mind me doing that. I'm about to finish up with it now and will be posting "for review" - would greatly appreciate your comments/suggestions on the article. Will definitely be acknowledging all assistance.

 

[neilparker62]

Hi again. I've written a second article which is a sequel to the first one above. I hope I won't tax contributors patience if I again request review ? Techniques used in measurement of battery internal resistance are expanded to measure low resistance generally. By simple ratio of voltages in a series circuit.

The article is entitled "The Poor Man's Milli Ohm Meter" and has been posted to the Insights development forum.