I have an OPUS BT-C3100 charger and it is very easy to check the mAh capacity of a single cell with it.
“Just set it and forget it” as Ron Popeil, The Veg-O-Matic TV pitch man used to say.
But, I found myself needing to determine the mAh (Ah) capacity of an 18V Ridgid drill pack. No way the Opus can help me with that.
First the back story.
Last week while traveling I came across a super deal on an 18V 4Ah Ridgid drill pack battery and fast charger combo. Separately those 2 items would cost about $150 but I got them on clearance for $49
The problem surfaced a few days later when I opened the package. At first the battery appeared to be used! I initially thought perhaps some dishonest customer had bought the package and replaced the new battery with one theirs and returned it. On second look, the battery looked kind of new but it wasn’t. And the battery level indicator built into the pack only had 1 light on of 4 (meaning empty) and it was flashing. I thought that was surely not a good sign.
So when I got back home I took it back to my friendly hometown HD to see what they could do for me. I knew that they couldn’t simply replace the combo pack because there would be none, this was a rare clearance special. I was hoping that they would just give me another new cell, but they wouldn’t do that either. They did offer to refund my purchase price, but I was not wanting to give up that good deal I got!
Then the gal in hardware pointed out that this battery pack appeared to have been glued into a demo unit. That is what they do sometimes do the prevent someone from removing it and walking out the door. “Shame on that store for repackaging it” she said.
Then she started talking like a BLF’er. She explained to me that this pack being new and having never been charged is probably going to be OK, why not take it home and charge it up. If it’s no good then we will send it back to Ridgid.
I knew what she had just explained was true and quite frankly I surprised that she even knew that.
But that for me would be inconvenient and time consuming. I really wanted to hang on to this deal so I decided to test this battery pack and if I thought it was actually undamaged, capacity wise, I would keep it.
That’s the back story, now on how to estimate the capacity of my possibly damaged or used drill pack. The tools I used were a 3 ohm 175W power resistor, a cheap voltmeter and a watch. Before I get into the details I have to explain a few things.
Here is a graph I pulled off the internet of a typical discharge curve for Li-Ion cell.
This graph though is not exactly the same graph we usually see. This graph plots Voltage vs Time. The reason I chose this graph is because when I discharge this 18V pack into the 3 ohm resistor, I will be measuring the voltage across the resistor. Because of Ohms law I = E/R and this case with R=3ohms, for each voltage reading I take I can calculate the current flowing through the resistor by dividing by 3.
Now my drill pack contains 5 cells in series, so the scale on the Y axis will be a multiple of 5, and if I divide each voltage reading by 3 ohms, the Y axis of this graph becomes Current.
It is important to realize that this new graph will have the same exact shape. This is important for what comes next.
Let’s go back and look at what the capacity of a cell really is. Let’s look at the units of the quantity. We usually measure the capacity of single 18650 cells in mAh, milli amp hours or in the case of drill packs Ah. 1Ah equals 1000 mAh. That quantity is the unit “Amps” multiplied by the a unit of time (hours)
Imagine the graph above. We have converted the Y axis quantity of volts to amps by dividing by 3 ohms. and the x axis is time in minutes.
BTW that red dashed line across the graph represents the recommended low cutoff voltage while discharging a single cell. My drill pack has a protective circuit inside that will shut down the entire pack when that cutoff voltage is reached for any single cell.
Looking at that graph above it may become apparent that the capacity of the cell is the area under the curve
But how do we calculate the area under that curve without using calculus?
The answer is we can’t, but we can estimate it! and it turns out we can estimate quite well and quite easily. Here’s how.
First of all I want to say that we humans have a remarkable ability in our brains to make estimates constantly in our daily lives without even realizing it. We do it when we slice a pie into equal pieces, when we toss a paper into a waste basket, or drive a car etc.
Here is a second picture of the graph above with a line drawn with a straight edge that was placed such that when that solid read line was drawn, that by eye (my estimation) there were equal areas in region “A” and “B”
If you will agree that the area in region A is approximately the same as the area in region B, then the area under the curve is approximately the same area as in the rectangle bounded by the horizontal and verticle red lines and the X and Y axis.
This is true because the rectangle does not include the area of region A but does include the extra area of region B. The 2 regions being equal, region B makes up for the area missed in region A
Now if all that is true, to estimate the capacity of my 18V drill pack all I need is a couple of data points.
Look again at the second graph above. When I adjusted that horizontal line so that regions A and B were equal, the red line intersects the discharge curve at approximately halfway, time wise, thru the discharge test.
So a simple “quick a dirty” way to estimate the capacity of a cell or drill pack is to discharge it to the low voltage cutoff, record the time to do so and get a measurement of the voltage halfway thru. Those 2 quantities are enough to give you a pretty good estimation of the capacity of the cell, or in my case drill pack.
Lets see how this worked for me and my drill pack. Remember, I want to determine if it has been damaged. It is supposed to be a 4Ah pack.
Here are my data points as I discharged the 18V drill pack through a 3 ohm resistor
minutes volts
0 ………. 19.8
2 ………. 19.3
12 ………. 17.9
20 ………. 17.3
21 ………. 17.3
24 ………. 17.0
25 ………. 16.9
30 ………. 16.7
33 ………. 16.5
38 ………. 16.2
41 ………. ?
Not very many data points, but only 2 of these numbers will be used.
I didn’t record what the voltage was when the pack shut down. But then that was not important. What is important is knowing that it was at 41 minutes. The other number that is important is what the voltage is halfway thru the run. At 20.5 minutes the voltage was 17.3 Volts
41 minutes and 17.3 Volts are the 2 points that determine the size of the rectangle. The area of that rectangle is the capacity of the drill pack.
The units of capacity is Amps multiplied by Hours
I = E/R = 17.3V/ 3 Ohms = 5.767A
41 minutes x 1 hour/60 minutes = 0.6833 Hours
Capacity = 5.767A x 0.6833 Hours = 3.941 AH (new pack is rated at 4.0AH)
Now I calculated these numbers out to 4 digits which is ridiculous, after all this is just an estimate. But what this did prove to me is that this drill pack is good, probably good as new.
So I decided to keep it, as is. 
