Check my math - Page 1
Forum section: electronics / beginners

author: BradC
author_rank: Super Contributor
timestamp: November 06, 2023, 04:51:16 am
content: G'day all,I bought a 500F super-capacitor bank from Aliexpress for use in battery tab welding. It's "a bit rough around the edges" and I was expecting the capacity value to be wildly inflated.I did a discharge test with an iMax B8 hobby battery charger, and from 14.8V to 9V I got 818mAh. That works out at ~2945 Amp/seconds (Ah x 60 seconds x 60 minutes).My back of the packet calculation for 500F and a 5.8V drop is about ~2900 Coulombs (as in it'll lose 2900 Coulombs to discharge the pack from 14.8V to 9V). This is close enough to my measured Amp/second value as to be well inside any margin of measurement error.Am I right to be pleased or have I made a basic error somewhere?

author: Konkedout
author_rank: Frequent Contributor
timestamp: November 06, 2023, 05:09:42 am
content: 2945 Ampere-Seconds (not Amperes/second) = 2945 Coulombs. This is important; is it misunderstanding or typo? I come up with 356 Farad(ays). But where I am right now it is Sunday. So you are off by 2 days.

author: jonpaul
author_rank: Super Contributor
timestamp: November 06, 2023, 07:56:09 am
content: Arithmetic:I = C dv/dtUnits seconds/volts/amperes/faradsno coulombs involvedj

author: Psi
author_rank: Super Contributor
timestamp: November 06, 2023, 08:06:49 am
content: Yep,500F at 500A would be 500A/500F = 1V drop per second.or500F at 100A would be 100A/500F = 0.2V drop per second.etc..So you just setup a constant current discharge, measure starting and ending voltage, and the time it took to get there.Then you can work out Vdrop per second, rearrange the formula and plug that in to work out capacitance as the unknown.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: November 06, 2023, 08:15:07 am
content: Yeah, be very careful to always make sure you're handling units correctly. Dimensional analysis works undeservedly well, when you treat unitsconsistentlyas algebraic symbols that can cancel out when multiplied and divided together.Then it is perfectly clear that "ampere-hours" (that's a hyphen indicating combination, multiplication; not a subtraction) means amps*hr, and 1 Ah * 60 min/hr * 60 s/min = 3600 As = 3600 C.It most definitely is not A/hr, a rate of change; this is far from a meaningless unit, but indeed is relevant when talking about inductance, as 1 H * 1 A/s = 1 V.Dimensional analysis also hints us in the right direction when units must be canceled out to dimensionless quantities (pure ratios) to use in arbitrary calculations, especially real-valued exponents, or trig functions. Or if you like, trig functions can be treated as taking an angular argument, so you often see "rad"(ians) as a unit in such calculations to make it clearer.Quote from: Konkedout on November 06, 2023, 05:09:42 amIncidentally, as long as we're talking about dimensions here: faraday is a unit of charge, most often applicable to electrochemistry, being the charge in a mole of singly-charged ions.And, just to ensure dotted tees and cross eyes -- units should be lowercase when spelled out, as they are not proper nouns (the tesla (unit) is named for Tesla (person)). When abbreviated, use the SI defined symbol.There should also be a thin space between the number and the unit. This is kind of annoying to write with normal ASCII, so zero or one (regular) space is fine. So, "500F" or "500 F" or "500 farads" would be fine. Formally, we would write \$500 \, \textrm{farad}\$ (quote this post to see my markup code), available since we have \$\LaTeX\$ enabled here.Tim

author: magic
author_rank: Super Contributor
timestamp: November 06, 2023, 08:25:41 am
content: Quote from: BradC on November 06, 2023, 04:51:16 amYes to bothYour units are mixed up as pointed out by many others, but the numbers seem to check out.

author: BradC
author_rank: Super Contributor
timestamp: November 07, 2023, 05:24:28 am
content: Quote from: jonpaul on November 06, 2023, 07:56:09 amFine. dv = 5.8v - dt = 1970s - C ~= 500F gives me an I of 1.472. The theoretical "I" was 1.5 so again, easily within the bounds of measurement error given what I was using.The definition of a Farad I looked up said the capacitance that changes 1V with one Coulomb, I figured working it out using Coulombs was the way to go, but your way works too.Edit : Got 500A using a 500A carbon pile, so all in all I'm pretty surprised and pleased. Plenty of current and capacity as rated, plus I learned about the importance of correct units

author: radiolistener
author_rank: Super Contributor
timestamp: November 07, 2023, 03:26:47 pm
content: Quote from: T3sl4co1l on November 06, 2023, 08:15:07 amunits of measurement named in honor of someone's last name should be capitalized.5 F, 5 mF 5 uF, 5 nF, 5 pF - are correct5 f, 5 mf, 5 uf, 5 pf - are incorrect5 V, 5 mV, 5 uV, 5 nV, 5 pV - are correct5 v, 5 mv, 5 uv, 5 nv, 5 pv - are incorrect

author: T3sl4co1l
author_rank: Super Contributor
timestamp: November 07, 2023, 03:43:17 pm
content: Quote from: radiolistener on November 07, 2023, 03:26:47 pmYou missed this part -- or perhaps I should've been more clear:QuoteIndeed 'f' is the symbol for the femto- prefix (10^-15).Tim

author: alligatorblues
author_rank: Regular Contributor
timestamp: November 08, 2023, 07:36:26 am
content: Quote from: T3sl4co1l on November 06, 2023, 08:15:07 am

author: T3sl4co1l
author_rank: Super Contributor
timestamp: November 08, 2023, 08:53:43 am
content: Quote from: alligatorblues on November 08, 2023, 07:36:26 amFarad is capacitance. Faraday is:https://en.wikipedia.org/wiki/Faraday_constantTim