Reading high currents on PCB: Hall effect sensor vs shunt resistor - Page 1
Forum section: electronics / projects

author: superKris
author_rank: Regular Contributor
timestamp: May 05, 2020, 03:46:45 pm
content: Hi All,I designed a PCB which features a Arduino that is controlling relays, reading currents, and sending data via RS422.Today I "completed" the software, but i'm not totally happy with the current measurement. I'm looking for opinions on how to improve.The PCB uses 3 types of current sensors.- INA219 via external 200A/75mv shunt. (works fine)- ACS712 via ADS1015 ADC. Needs to read currents up to 20A- ACS756 via ADS1015 ADC. Needs to read currents up to 40...50AMy main problem is with the bidirectional behavior of the ACS hall sensors. The zero current output of these is 0,5 * VCC. The ADS1015 has a internal voltage reference.This causes the readout of the ACD to be very different depending on the VCC. A few mV difference can results in a few 100mA readout results.For my application i dont mind a few % deviation on full scale, but i do need 0A to be displayed as 0A (or at least close to this)The schematic:ACS current sensing.PNG(96.52 kB. 1010x855 - viewed 252 times.)And here is the relevant code im using:Code:// For analog current sensors some math has to be done to convert raw ADC output to real voltage, and next to current. The formula for this is: (ADCvalue * LSBsize - 2,5) * const - offset// LSB size depends on ADS1015 setting. A FSR (full scal range) of 6,144V (default) provides a LSB of 0,003 V. A FSR of 4,096 proveds a LSB of 0,002V, but limits the readable range of the current sensors// The constant is based on scaling of current sensors: ACS712-20A = 10, ACS712-30A = 15, ACS758-50A = 25. Formula: 1000/sensitivity (mV/A). All sensors are bi-directional. Remove -2.5 for unidirectional// The offset is to compensate for the behaviour of the ACSxxx sensor caused by fluctuations in VCC. Enter a float to set to zeroIsol = (ADS1015output.getSingleEnded(0) * 0.003 - 2.5) * 15 + IsolZeroOff; // Read ADC output, do math, and store to float. See text above for math explanationIchar = (ADS1015output.getSingleEnded(1) * 0.003 - 2.5) * 15 + IcharZeroOff;; // Read ADC output, do math, and store to float. See text above for math explanationIsys = (ADS1015output.getSingleEnded(2) * 0.003 - 2.5) * 25 + IsysZeroOff;; // Read ADC output, do math, and store to float. See text above for math explanationIacc = (ADS1015output.getSingleEnded(3) * 0.003 - 2.5) * 25 + IaccZeroOff;; // Read ADC output, do math, and store to float. See text above for math explanationWith the offset set to 0 and a VCC of 4,964V I get the following output.Isol: -0.1950 A. Raw ADC output: 829 (Raw ADC output at 0A should be 833 for 2,5V/0A. The LSB size is approx 0,003V and 0,03A)Ichar: -0.1950 A. Raw ADC output: 829 (same as above)Isys: -0.5500 A. Raw ADC output: 826 (Raw ADC output at 0A should be 833 for 2,5V/0A. The LSB size is approx 0,003V and 0,075A)Iacc: -0.7750 A. Raw ADC output: 823 (same as above)I can compensate for this using the offset, but this offset changes with every change in VCC. How can i do this in a better way?- Use a very accurate 5V reference for VCC, so my 0A is stable- Add a extra ADC to measure actual VCC and calculate a dynamic offsetI'm not a huge fan of both options, so now i'm considering changing the setup to shunt resistors and additional INA219 sensors.There is however a disadvantage in using shunt resistors. Even with a low resistance like 50A/40mV, i have to dissipate 2W of power. There will be 2 of these 50A measurements, and there are 2 additional 20A/40mV shunt that will disipate up to 0,8W.While its not likely to have all currents at maximum often, the dissipation can run up to almost 6W in total, but even at 2 or 3W i will be adding heat to a PCB that has to transfer a lot of current. I'm planning to do a dual 2oz trace on both sides, but this is barely enough.Additionally, i have no experience at all with PCB mounted current shunts. What shunts with a 50A/40mV are available, and how accurate are these? I can imagine the (position of) soldering on the PCB will influence the resistance.Also i like the ACS756 for their beefy solder legs. I guess a though hole shunt will be preferred to SMD type with a lot of vias between the layers.What do you guys recommend? Stay with the hall effect sensors, or make new PCBs with shunt resistors?If shunt resistors, Can you link any suitable shunts?

author: nctnico
author_rank: Super Contributor
timestamp: May 05, 2020, 04:00:45 pm
content: The simplest solution is to make sure your ADC's reference is powered from the same supply as the HAL sensor chip. That way the midpoint of the HAL sensor is always aligned with the midpoint of the ADC reading. ADCs inside a microcontroller typically have this. BTW: did you think about measuring the voltage drop across a PCB trace? If you add an NTC to measure the temperature of the board you can compensate for the temperature coefficient of copper and still get a reasonably accurate reading. You'll need a (low offset) current sensing amplifier chip but it is a relatively cheap and reliable solution especially for very high currents (10s of Amperes). Something else you need to consider are significant digits. If your range is 50A and your accuracy is 2% then your resolution is about 1A. All in all you shouldn't display the current with a higher resolution than 1A. So a 400mA offset should be rounded to read 0.

author: guenthert
author_rank: Frequent Contributor
timestamp: May 05, 2020, 04:01:50 pm
content: You haven't told us, whether this is a one-off project or a larger production run. If the former, than I don't think you'd need a highly accurate 5V source for your sensors, just a stable one. The latter typically excludes post-production calibration and you'd have to get precision parts to stay within the error budget. Speaking of which -- "but i do need 0A to be displayed as 0A (or at least close to this)" -- how close is close?

author: superKris
author_rank: Regular Contributor
timestamp: May 05, 2020, 05:09:43 pm
content: Quote from: nctnico on May 05, 2020, 04:00:45 pmThanks for your reply! Unfortunately the ADS1015 does not have a way to use a external reference. I would need to switch ACD but i really like this one for its great libraries and easy use. The ACD's on the uC are already in use, and i dont like their accuracy (Arduino nano).I'm not sure about using a PCB trace. I dont know how accurate these are and i want to use large copper areas instead of normal traces with al components very close together.Quote from: guenthert on May 05, 2020, 04:01:50 pmFor now its just for me, but i am designing it as a commercially viable product that, if it works, i will try to sell of give away the design for free. Batch size will be low. A few pcs to 10 or a multiple of that.Lets say a error of 5% is fine, but 0 should be close to 0. I want to be able to see the difference between 0 and lets say 200mA. The current parts offer a resolution of 30/ 75mA. Maybe a 2* LSB accuracy would be acceptable but i do think the resolution is low enough to be spot on.

author: David Hess
author_rank: Super Contributor
timestamp: May 05, 2020, 06:47:07 pm
content: Quote from: superKris on May 05, 2020, 03:46:45 pmThe hall sensor is intended to be used as half of a Wheatstone bridge providing a differential signal insensitive to supply voltage. A voltage divider across the supply voltage provides the other signal and then either an ADC with a differential input is used or an instrumentation amplifier can convert the differential signal to a ground referenced signal.QuoteThe supply voltage itself does not need to be stable.QuoteOr use an ADC with differential input, or use an instrumentation amplifier to produce a ground referenced signal.Quote from: nctnico on May 05, 2020, 04:00:45 pmIt is the offset which is changing with supply voltage and not the gain.

author: ejeffrey
author_rank: Super Contributor
timestamp: May 05, 2020, 07:03:14 pm
content: This ADC has a differential input. Make a 2:1 resistor divider from Vcc and connect that to the (-) input of the ADC. Your chosen ADC is buffered and has a high input impedance so you should basically be good to go.

author: superKris
author_rank: Regular Contributor
timestamp: May 05, 2020, 09:19:07 pm
content: Quote from: ejeffrey on May 05, 2020, 07:03:14 pmIf i'm not mistaking a voltage divider would need to be extremely accurate. Exactly the same 0,5 * VCC as the Hall effect sensor. At a difference of 3mV (1 LSB) I would need to do a analog adjustment of the Wheatstone bridge or do a digital adjustment. However, once set the reading should be fine even with a changing VCC.Would it be possible to use to do a differential input with VCC and the analog out of the Hall sensor? This way there shouldn't be any offset right?Although i do not fully understand why, the ADS1015 is actualy 12bit in differential mode, and 11 bit single ended, so i actually gain some resolution. This way.The only downside is that i would need 2 instead of 1 ACD as i need to measure 4 sensors. This not a huge issue because i have enough space on the PCB, and they are reasonably cheap.A small downside would be that these ACD's need approx 8ms to read. 2 of them + the INA219's would add up to approx 25mS. I dont think its a huge problem for my code but i hope it wont mess with my RX code. Also the packages are a pain in the ass to solder!I have however heard nobody about using shunt resistors and more INA219's instead. What do you guys think should be the preferred solution?

author: M0HZH
author_rank: Regular Contributor
timestamp: May 05, 2020, 10:42:46 pm
content: I use ACS713 in a small series product for measurements up to 22A DC or so. At every startup, the software averages 100 readings from the Hall sensor before turning on the load; that average is used as the offset and the drift is minimal with a good 5V regulator.Would that work ?

author: superKris
author_rank: Regular Contributor
timestamp: May 06, 2020, 07:23:24 am
content: Quote from: M0HZH on May 05, 2020, 10:42:46 pmNot really im afraid. For most of the current sensors there is no way to switch off the load.

author: Miyuki
author_rank: Frequent Contributor
timestamp: May 06, 2020, 07:46:51 am
content: Quote from: superKris on May 05, 2020, 03:46:45 pmThey used to have unidirectional variants of them if you need to measure just to one polarity

author: fourtytwo42
author_rank: Super Contributor
timestamp: May 06, 2020, 08:52:41 am
content: Your problem is using a ratiometric sensor with an absolute ADC. Simple solution use the internal Arduino ratiometric ADC's that you dont like for the current sensors and use the absolute ADC for whatever you are currently using the internal Arduino ADC's for.The supply voltage for the sensors and Arduino must be exactly the same, ie +5V from the same regulator for both and set the Arduino reference to Vcc.As for the offset that simply means you have one bit less resolution than you thought you had. If you want to increase gain use a r-r i/o op-amp.As someone else said you can easily take care of fixed offsets (that will also be present in the ADC) by a calibration period with no load.

author: Jeroen3
author_rank: Super Contributor
timestamp: May 06, 2020, 09:51:37 am
content: Quote from: superKris on May 05, 2020, 03:46:45 pmAdd deadband on the visualization. Those ACS sensors aren't that amazing. They're mostly easy.You might get magnetic offset in the future not reading zero correctly again.

author: superKris
author_rank: Regular Contributor
timestamp: May 06, 2020, 01:52:38 pm
content: So i think i now realized i can not use the differential input with the VCC. I really need the voltage divider you guys are talking about, and it needs to be adjustable by a adjustable resistor, or i can adjust in software, but there will be mostly theoretical gain error.Or i need a different ACD. Can you guys suggest one that:- Has a external reffrence- Has at least 4 inputs- At least 11 bits output- 12C interface- And a reasonable Arduino libraryQuote from: Miyuki on May 06, 2020, 07:46:51 amIt might indeed help, but these sensors are very widely available and that also makes them cheaper. There is also some advantage in them bering bidirectional, although i could easily do without.Quote from: fourtytwo42 on May 06, 2020, 08:52:41 amThanks for your input! the reason i dont like the Arduino ACD's is that these are only 10 bits, and in previous project i really did like their stability. 10 bit would be a resolution of 50 and 125mA with a less than stable LSB.Quote from: Jeroen3 on May 06, 2020, 09:51:37 amFor my application i do wanna it to show currents of 100mA. 50 or 25mA would be even better.But you are right that these ACS sensors are far from perfect. The ACS758 inst that cheap either, so that is why i'm considering to take these out and switch to shunts with a INA219. I dont really know how to with with PCB shunt, and i can think of some disadvantages like i wrote in my first post.So generally speaking: What method would you guys prefer for measuring currents up to 50A/12V on a PCB?

author: David Hess
author_rank: Super Contributor
timestamp: May 06, 2020, 03:25:35 pm
content: Quote from: fourtytwo42 on May 06, 2020, 08:52:41 amThe hall effect sensor he is using is not ratiometric; its gain is fixed. What changes is its offset which is always 1/2 of the supply voltage.

author: fcb
author_rank: Super Contributor
timestamp: May 06, 2020, 05:53:00 pm
content: ACSxxx sensors aren't actually very good - you'll probably get within your few% though. Zero drift will be your #1 problem to solve with anything hall based.I'm assuming your application is DC and requires isolation - looking at your PNG then it looks like a a low voltage system (mention of accessories, chargers etc..) - in that case you could easily use current shunt shunt resistors and float the differential measurement?Either way, I would defintley look at using shunt resistors rather than hall sensors if you want a reliable ZERO. Texas make some IC's worth looking at if your system is lower voltage DC: LMP8480, INA282 range.

author: superKris
author_rank: Regular Contributor
timestamp: May 06, 2020, 06:57:13 pm
content: Quote from: fcb on May 06, 2020, 05:53:00 pmI'm already using the INA219 for external current shunt and voltage measurements. Incredible little chip.However, like I wrote i fear about the dissipation that will come with that. I'm hoping to run 40A (with peaks of 50) trough a PCB with 2oz copper "traces" on both sides. Below you can find a drawing of what it currently looks like. Its a automotive application (RV) so temperatures can get high easily.If i take for example a INA219, the lowest shunt voltage setting is 40mV. Even that is 2W at 50A. I have 2 of those + 2x 20A shunts. While i doubt the total disipation will go over 3W often, i have my doubts about adding that heat to a PCB that can barely hold these currents in the first place.I'm aso VERY unfamiliar to using these kinds of shunts, and i have no idea about their accuracy, and the way to mount them.

author: ejeffrey
author_rank: Super Contributor
timestamp: May 06, 2020, 07:15:39 pm
content: Quote from: superKris on May 05, 2020, 09:19:07 pmWell, .1% resistors or even .01% are not that expensive, but that is unlikely to be the most important factor. The Vcc/2 offset on chip is probably not that accurate either and even if it was the offset and drift of the sensor itself are going to be relatively large. A voltage divider is going to get you about as good as you can do with that sensor. Zero calibration will help with the intrinsic offset, but fundamentally you aren't going to get a great zero value on a hall sensor. Even a unipolar sensor won't help much: it gets rid of the Vcc/2 divider accuracy problem but doesn't really address the offset and drift of the sensor itself.Can you do periodic zero calibration? Either deliberately stop the current periodically or just rely on times of known zero current such as at startup.

author: fourtytwo42
author_rank: Super Contributor
timestamp: May 06, 2020, 07:53:06 pm
content: Quote from: David Hess on May 06, 2020, 03:25:35 pmOopps yes sorry David your right, it's been a while since I used the things! Actually I much prefer the LEM, much more stable and less noise sensitive, as I use it unipolar I just follow it with a precision diff amp to remove the offset (the LEM has a reference output at what it thinks is 1/2vcc so it tracks nicely).

author: superKris
author_rank: Regular Contributor
timestamp: May 06, 2020, 08:48:45 pm
content: I'm afraid any periodic calibrations will be difficult.I really have many doubts if hall sensors remains the way to go. They are awesome at not dissipating any real heat, they are getting to be a pain in the ass.Meanwhile i have been searching a lot for suitable shunt resistors but i can only find them at ridiculous prices of € 5 to 20 per shunt. And basically I have not been able to find any with a suitable rating: 750uOhm or 50A/40mV.I was only able to find this SMD type, but i dont really understand how this would work on the suggested 20oz board at 50A. Even with a shitload of vias... Wil it hold the current?http://www.farnell.com/datasheets/2710720.pdf?_ga=2.148078839.1947980846.1588791907-1152630265.1588791907

author: Vovk_Z
author_rank: Super Contributor
timestamp: May 06, 2020, 11:25:00 pm
content: Quote from: superKris on May 06, 2020, 06:57:13 pmQuote from: superKris on May 06, 2020, 06:57:13 pmYou may divide one shunt into several parallels.But is there a strong need to put shunts onto the PCB? 40-50 Amps looks good for external shunts.

author: ejeffrey
author_rank: Super Contributor
timestamp: May 07, 2020, 01:49:24 am
content: Here's one for a dollar in small quantity.https://www.digikey.com/product-detail/en/te-connectivity-passive-product/TLR3A30ER00075FTDG/A131798CT-ND/8603928There are a lot more options if you pick 1 mohm or 500 uohm.50 amp is a lot but not unreasonable. 2oz copper on top and bottom with wide traces and lots of vias and you should be fine. Still an external shunt may be an easier option.

author: Jeroen3
author_rank: Super Contributor
timestamp: May 07, 2020, 06:16:00 am
content: 50 Amp is territory for LEM sensor modules. Where you can just feed a wire trough a ct.Or Sensitec, but unfortunately they obsoleted the integrated solution,CMS3050, but if you can still get a few... They're amazing! Zero drift spot-on accuracy, good resolution (1/1000th of range, no external magnetic influence.Else just get a piece of wire as shunt and calibrate it. Just like they do in those high current power supplies.There's a teardown on the channel somewhere of a high current power supply, but I can't find it...

author: superKris
author_rank: Regular Contributor
timestamp: May 07, 2020, 09:37:33 am
content: Quote from: Vovk_Z on May 06, 2020, 11:25:00 pmThank you, i was struggling a bit with putting shunt parallel. Ohms law tells me that with equal resistors in parallel the current must be the same. However i can remember reading some articles about current always taking the path of least resistance, so i can imagine that even the slightest imbalance might cause the current to flow trough the lowest shunt.Anyway, a external shunt is out off the questions. The whole idea is that i want tot move a lot of loose components like relays, fuses, and current sensors.Quote from: ejeffrey on May 07, 2020, 01:49:24 amThanks. I guess 500uohm could work, but i can imagine the output would be very sensitive! 0,1A would be 0,50uV. I hope a INA219 would be up to this. I guess its mV vs dissipation.Anyway, i'm having a little trouble imagining the physics of 50A running trough such a small SMD component. I guess i could take 2 of 1,5mOhm and put them parallel on both sides of the PCB, but that is still a very small pad its sitting on!My mind says i need huge thick trough hole shunts to pass that amount of current....Quote from: Jeroen3 on May 07, 2020, 06:16:00 amIsnt that more or less what i'm already using? Anyway, such current transducers are expensive, large, and not as easy to mount. No problem for a single build, but i'm hoping to sell the product or give away the disign for free in a later stage.Thats sensitec looks great, but i cant find any sellers, and it looks kinda expensive.I think i have seen that video. I think shunt like those might be suitable, but they are not available in low quantities, or the price goes up to € 10,- which i think is ridicules

author: fcb
author_rank: Super Contributor
timestamp: May 07, 2020, 10:34:50 am
content: So we use 20ppm/oC tempco current shunts in our compact power analysers (CPA) and we derate them ALOT to get stability over current range -HOWEVERif you can afford a few % error and a factory calibration cycle then why not use the actual PCB traces as the current shunts - you will likely need a bit more accuracy than the tempco of the copper PCB will allow (4000ppm/oC!) - you can measure the actual temperature of the shunt (MCP9701) and apply tabled compensation (which would easily get you under a few %).

author: exe
author_rank: Unknown
timestamp: May 07, 2020, 11:07:43 am
content: Quote from: superKris on May 07, 2020, 09:37:33 amNo, not at all. They may not equally share the load, but this doesn't mean they don't share it at all. A random article from the Internet:https://www.electronics-tutorials.ws/resistor/res_4.html. Basically, since resistors are in parallel, voltage accross them is identical. So, they share currents as following: 1/Itot = 1/Ir1 + 1/Ir2.You need to route kelvin connection to them, may be add small resistors in series with sense leads (in case one shunt goes open and current may decide to flow through sense leads, not sure about that, what's your opinion?).

author: Siwastaja
author_rank: Super Contributor
timestamp: May 07, 2020, 12:08:19 pm
content: Quote from: superKris on May 07, 2020, 09:37:33 amJust clear that bullshit from your head. Such "information" is indeed often seen, even by teachers, and is very damaging because it easily gets stuck in your head. Obviously, it is not true, as shown by simple analysis with the Kirchoff voltage and current laws.Something similar to what you describe - all current going through one device due to even slight imbalane - does happen with semiconductor devices which have exponential current vs. voltage characteristics, and which may have the temperature coefficient the "wrong way", so that one device using more current causes it to start hogging even more current. But these devices are not measured using the unit of resistance.

author: ejeffrey
author_rank: Super Contributor
timestamp: May 07, 2020, 06:10:58 pm
content: Quote from: superKris on May 07, 2020, 09:37:33 am50 microvolt/ 100 mA. The INA219 has a typical DC offset of 10 uV, so equivalent to 20 mA. That's pretty good. The worst case is 50-100 uV, it depends on your actual target offset.QuoteIts just not that big a deal. A lot of the rules of thumb for current density are based on long traces with very conservative temperature rises such as 10C. For something a short trace just the length of a pad and if you are willing to tolerate a bigger temperature change you can push a lot more current than the conservative estimates suggest.Using copper traces for the shunt as suggested above is also an option. It is more complicated since you need to add temperature correction but cheaper since a temperature sensor is likely cheaper than a good current shunt resistor.

author: engrguy42
author_rank: Frequent Contributor
timestamp: May 07, 2020, 07:37:54 pm
content: Quote from: Siwastaja on May 07, 2020, 12:08:19 pmI'm cornfused....A true calculation of resistance includes considering the temperature coefficient of resistance, doesn't it? And if it's negative like semiconductors, that will change the value of resistance. How is that BS?

author: ejeffrey
author_rank: Super Contributor
timestamp: May 07, 2020, 08:19:30 pm
content: What he is referring to is the common misunderstanding by those new to electronics of the phrase "current follows the path of least resistance" to mean that when there are resistors in parallel the current only flows through the smaller one. In reality we know the parallel combination of to resistors is smaller than either and the "least resistance" path is to flow through both.

author: superKris
author_rank: Regular Contributor
timestamp: May 07, 2020, 08:19:45 pm
content: Thanks all, I have done a lot of reading based on all your tips.I don't think using the traces for current measurement is a bad idea, but i woud need to do a lot of testing and redesign. I think it will be a little to tricky for me at this point, and i do have limited time.So with everything i learned I think I think have the following option:Hall effect sensorsI can stick with my ACS712/ACS758 sensors. However to get them stable i would need to redesign to a differential ACD setup, as i prefer not to use the Arduino's ACD's. A solution would be adding another ADS1015 and a voltage divider with either a potentiometer, or precision resistors or a software offset in the uC's code.Current shuntThe INA219 is a great device. Extremely easy to use and seems reasonably stable. I would need 1 per channel as chips like the INA3221 require higher shunt voltages. A small advantage of this might be that I can place them very close to every shunt. A 0,0015mOhm shunt would be perfect. A single one will cover the 0-20A range nicely. A double one (On both sides of the PCB) will be perfect for the 0-50A range.I made a table to compare the advantages and disadvantages. I hope i got the data right.So looking at this, there seems to be some advantages to switching to shunts. I'm not sure how these translate into the real worldFor now i wanna assume the 2oz traces ans the small SMD shunt are up to the task of transferring the 50A. The dissipation however will be a lot higher for the 50A shunts. I fear the PCB traces and components will already add more heat than i would prefer. Will the additional dissipation be a problem?Also a 0-37mV signal is MUCH more sensitive for disruption than a 0,5-4,5V signal. How stable can i get the signal at a LSB size of 10uV? I gues i dont really need that level of precission, but 40uV/50mA would be nice to have. Do you guys this is possible, or will there be to much noise etc.

author: Siwastaja
author_rank: Super Contributor
timestamp: May 07, 2020, 08:31:35 pm
content: Quote from: engrguy42 on May 07, 2020, 07:37:54 pmIf a resistor has such strong negative temp coeff that it causes practicallyallcurrent go through one resistor with onlyminorimbalance in resistance, such part is crappy beyond imagination and could hardly be called a resistor; it would be asemiconductor, or maybe an NTC.I was commenting about the phrase "current flows through the path of least resistance", which is just simply untrue and makes no sense whatsoever. Whoever came up with that wasn't thinking temperature coefficients or other sophisticated details; in fact, they just were not thinking at all, and then it stuck. Current is shared between the resistive paths in a simple linear fashion, I = U/R where U is the same over all paralleled resistors. So if you apply 1V over 0.9 ohm and 1.1 ohm resistors, the currents are 1.11A and 0.91A, respectively. The sad thing is, this is so easy to analyze properly that no one needs to invent such a "helpful" phrase.

author: engrguy42
author_rank: Frequent Contributor
timestamp: May 07, 2020, 08:43:32 pm
content: Quote from: ejeffrey on May 07, 2020, 08:19:30 pmAAAAhhhhh, that's what he meant. I never considered that some people think that ALL current flows thru the smallest of two resistors in parallel. Thanks.