Now as a side note, if we were interested in the total energy contained in the cell, we would need to look at the electrical power expended in the test (which is not the same thing as the charge expended). This Riemann sum is performed until the cell voltage gets below a threshold, then it is stopped, cause that's all the usable charge the cell has (without draining the cell beyond recommend safe limits). The idea of a Riemann sum is that the positive errors cancel out the negative errors, and it all washes out to be pretty close. In the Riemann sum picture (with all the vertical lines), sometimes the q is a little big, and sometimes it is a little small. We can just sum up all of the small capacities to find the large capacity. In terms of capacity, we use short time intervals (rectangle width) and multiply each of those with the current (rectangle height) to find a small amount of capacity expended in that time interval. In short, we can look at a plot and break it up into a bunch of thin rectangles, calculate the area of each rectangle (width times height), then add all the small areas together. Problem is, I didn't really want to do “proper” integration, so I figured I'd take a shortcut I used a thing called a Riemann Sum to perform a simple stand in for integration. time, the area under the curve would represent capacity (milliamps times hours gives milliamp hours). If we integrate current over time, we can find the exact capacity (Q= ∫ I dt), because if we plot a graph of current vs. ![]() The solution to this conundrum is to use calculus. This issue comes in when we realize that the current is not likely to stay constant, but rather start off high, then with dropping cell voltage, decrease drastically. ![]() This is a solid and simple technique, but it will only give rough values, but not a reliably accurate value. If we had a constant current, we could just run that current until the cell gets below the minimum voltage, then multiply the current times time, and we would have a rough approximation of capacity (Q=I*T). So really the capacity of cells is given in Q, the amount of “usable charge” they have in them, or, really, the number of electrons that cell can push through itself in a single discharge cycle. Milliamps are units of current, and hours are units of time, and when we multiply them, we get charge. The capacity of a cell is usually given in milliamp hours (mAh). This whole step is theory, so if you just want to get it running, skip on to the circuit. A car battery, laptop battery, or 9 volt are all batteries, because they contain multiple cells. So, a D, C, AA, AAA, and an 18650 are all cells. Before I go on, I'm going to distinguish between “battery” and “cell.” A cell is a single unit of fancy stuff that uses chemicals to store electrical energy. I re-assembled the circuit, but I added a few features, namely an LCD screen, as well as a cell resistance check. This instructable was originally published in 2014, but has since been rebooted as I wanted to test another batch of batteries. This project aims to do just that: measure the capacity of a cell using a real load until the cell goes dead. The problem is that, when getting li-ion cells from different sources, you might want to know the capacity of the cells you harvest, especially if you will be using them in series. ![]() ![]() They are super handy for flashlights and all kinds of projects. I like to use lithium ion cells because they hold a lot more power than "regular" rechargeable cells, and they can be harvested for cheap or free from discarded laptop batteries.
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