Which Resistor to Use with this LED?

By on October 9, 2015
resistor for led

 

 

 

 

 

 

 

 

led resistor

This is a very simple question, so simple that we usually don’t think too much about it and use whatever we know is working. The voltage might be 5V, 9V, 12V or any other. We know we have to insert a resistor in series with the LED to limit the current. What should be the value of this resistor?  If you browse the Internet to see what other people are doing you will find a wide range of opinions:

For 5 V, people use values ranging between 150 Ohms and 2.2 K. Many use 330 Ω!

For 9 V, people use values ranging between 330 Ω and 1.5 K. Many use 470 Ω!

For 12V, people use values ranging between 470 Ohms and 3.9 K. Many use 1K!

And so on… And the most interesting is that all those values seem to work… somehow. As long as the LED is ON and bright, people seem to be happy!

But is it optimal? Which one is the best choice?  If it works, does it matter?  To answer those questions we need to do some testing. The calculation indeed is very simple, it is only another application of Ohm’s Law:

led circuit

To calculate R, you just need to know the values of VF and IF which depend on the type of LED you selected and the brightness you want.

You will find a large number of “LED Resistor Calculators” on the Internet. They will ask you to enter VF, IF and VCC and will apply those value to the above formula. Some will suggest values if you don’t know them, unfortunately many will suggest 20 mA for IF!

Finding the correct values takes a little bit of investigation and this is what we are going to do in this article.

Forward Current (IF) vs. Forward Voltage (VF)

forward current vs forward voltage

A LED characteristic looks like the characteristic of any other diode. If you apply a small voltage across the LED, starting with zero and increasing slowly, there will be no current (or very little) until the voltage reaches a certain value (around 2 V for most LEDs), then the current increases sharply as the voltage increases (make sure you have a resistor in series to limit the current). Most diode manufacturers specify VF as the voltage across the Diode when the Forward Current (IF) is around 20 or 25 mA.

We are used with silicon diodes where VF is around 0.6 to 0.7 Volts. However, for LEDs VF is higher, around 2V for most LED’s and up to 3 to 3.2 V for some types of LEDs. There is not much you can do regarding VF as it depends on the type of LED you are using. All what you need is to know it or, if you don’t know it, to measure it!

How to select IF?

how to select if

The value of IF depends on the luminous intensity you want. The relation between the Forward Current and the Luminous Intensity is another LED’s characteristic as shown in this picture. The Luminous Intensity is usually given as a relative value compared to what it would be when IF = 20mA. On this graph, for example, we see that when IF = 10mA the Luminous Intensity is half of what it is when IF = 20 mA. Indeed for this particular LED the characteristic is almost linear and you will find out that it is the same for most LEDs.

If this is the relative value, what about the “real” value of the Luminous Intensity? It is usually expressed in mini candela (mcd) and also expressed in function of the viewing angle and wavelength. This data is presented on different graphs and tables in the LED Datasheet. It is beyond the scope of this article but could be an interesting topic if you want to use the LEDs for other applications than just indicate the presence of a voltage… It is also useful to compare different types of LEDs.

So, how to select the right value of the Forward Current? For our applications we want to use as less current as possible for a reasonable brightness. I tend to be a bit greedy with the current allowed for the ON/OFF LEDs in my projects and would never go up to 20 mA! For a long time, 10 mA maximum was my standard but now, with modern LEDs 5 mA maximum became my new standard. If the circuit is low power and needs to work on battery I would go for less current. Some LEDs still provide sufficient brightness under 1 mA or less.

To illustrate the above I put a few LED’s from my junk drawers under test, and checked how they behave, starting with 5 mA and then looking at what happens when we change the current. All it takes is a variable power supply, two multi meters and a resistor. Of course also the LED to be tested:

led project

You may wonder why, for most of those LEDs, there is no visible change in brightness between 5 mA and 10 mA as the Luminous Intensity is supposed to double based on the graph we have just seen? The reason is because the brightness perception of the human eye vs. the luminance is not linear. The human eye is more sensitive at low luminance than at high luminance.  We can see this by the fact that the LED’s brightness visibly increases when we increase the current from zero until a point after which it doesn’t seem to increase any more, even if we double the current. This is represented by the graph below.

led graph

For example, this blue LED is already very bright at 5 mA, then we do not see much difference if we increase the current up to 10 mA or more.

test led

This red LED already provides a reasonable brightness with only 1 mA!

testing led

And this is the one I will select for my project! I will settle for 2 mA. What will be the value of the resistor for 12 V? If you found 5K you are correct. I will select a resistor of 4.7 K to be a little bit on the brighter side.

Here it is with 12 V and 4.7 K resistor:

check led

Can we use LEDs for AC voltages?

led for ac voltage

This is a question many people would ask. Diodes usually can stand a certain amount of reverse voltage without breaking down. This maximum reverse voltage, for example, is 75V for the all too famous 1N4148 diode and much higher for rectifying diodes, which can stand up to several hundred Volts. The maximum reverse voltage of LEDs, however, is very low, usually around 5 V! If you connect a LED, with its serial resistor, directly to an AC voltage, for example 12 VAC, your LED will be damaged during the negative half period of the AC voltage. During this half period the voltage will be reversed. The current in the resistor will be very low as the LED doesn’t conduct, so the voltage dropped across the resistor will be low as well. The reverse voltage across the LED will be nearly equal to the peak AC voltage, permanently damaging the LED. But no panic, there are a few solutions. One of the solutions consists of connecting a diode (reverse polarity) in parallel with the LED as shown in this picture. The diode will clamp the reverse voltage to 0.7 V, protecting your LED. 

What about the resistor’s power rating?

This is a point that is often overlooked, because the power dissipated in the resistor is usually very low and we tend to think that any size of resistor will do. Not always though; it is important to consider the resistor’s power rating if you use very small resistors, such as 1/8W or SMDs. Let’s take an example of a LED under 12V for which we selected a Forward Current of 5 mA:

led formula

A 1/8 W (125 mW) resistor cannot be used and even a ¼ W resistor (250 mW) would be a bit too close for comfort!

Conclusions

LEDs are not all the same. We often buy them in bulk without knowing their exact specifications and we tend to use more current than necessary. For low power battery operated circuits you want to make sure that the LED used to indicate that the circuit is ON doesn’t use more power than the circuit itself! For other applications, where it doesn’t seem to matter much, it is good engineering practice to ensure that you don’t use more current than needed.  In any case it is useful to know the basic characteristics of your LEDs, and it is so simple to measure!

geraldmusy

 

 

 

Penang,

Gerald Musy

Please give a support by clicking  on the social buttons below. Your feedback on the post is welcome. Please leave it in the comments.

P.S-  If you enjoyed reading this, click here to subscribe to my blog (free subscription). That way, you’ll never miss a post. You can also forward this website link to your friends and colleagues-thanks!

You may check out his other article below:

http://www.jestineyong.com/harmonics-and-distortion/

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50 Comments

  1. Albert van Bemmelen

    October 9, 2015 at 1:16 pm

    Very nice article, you explained it very Well! I myself used this theory to fix my brothers doorbell light. The little light bulb inside his transparent pushbutton often was defect. And since over the pushbutton there was 14V DC from a doorbell melodie-generator it was only natural to replace the little lightbulb by a white LED with a resistor of about 520 ohm in serie. And white Leds like the Blue leds need around 4V at 20-30mA so about 10V stand over the 520 ohm resistor. And 10/520 = 5/260 1/250 gives about +4mA, times 5 is just about 20 mA. And it only gives light when the Pushbutton is not pushed. So if someone uses the doorbell pushbutton the light immediately stops and it also could indicate for deaf visitors that they are heard.

    Likes(4)Dislikes(0)
    • Gerald

      October 9, 2015 at 9:18 pm

      Thanks Albert. Yes, replacing small bulbs with LEDs is the way to go. Today there are white LEDs with very high brightness for a very low current. It will also be much more reliable.

      Likes(2)Dislikes(0)
      • Albert van Bemmelen

        October 10, 2015 at 4:49 pm

        Yes indeed Gerald. Only the plastic in which the Led is capsulated (the epoxy ?) deteriorates in time why the intensity and brightness also weakens. That why they in the new power leds use silicon based caps if I am informed correctly. But in that time it happens, I probably had already replaced a hundred new little lightbulbs.

        Likes(1)Dislikes(1)
  2. Muhammad Akhlaq

    October 9, 2015 at 2:15 pm

    Very well explained.

    Likes(1)Dislikes(0)
    • Gerald

      October 9, 2015 at 9:19 pm

      Thanks for your support Muhammad.

      Likes(0)Dislikes(0)
  3. Robert Calk

    October 9, 2015 at 3:15 pm

    Nice article, Gerald.

    Likes(0)Dislikes(0)
    • Gerald

      October 9, 2015 at 9:24 pm

      Thanks Robert. I am always looking forward to see one of your excellent articles but haven't seen any for quite a while. Hope you are well and still enjoying electronics. Keep sharing.

      Cheers,
      Gerald

      Likes(1)Dislikes(0)
      • Robert Calk

        October 10, 2015 at 1:25 am

        Hi Gerald,
        Yeah, it's been pretty slow around here. I have a couple of projects in the wings right now. One is a Samsung 46" LCD TV.
        In my article, "Low voltage Polarity tester", I have 2 LED's soldered in reverse parallel so that if the voltage you are testing is AC, both of the LED's will light.

        Likes(1)Dislikes(1)
        • Gerald

          October 10, 2015 at 11:09 am

          Hi Robert, thanks for your feedback.
          Cheers,
          Gerald

          Likes(1)Dislikes(0)
        • Anthony

          October 10, 2015 at 4:24 pm

          Hi Robert...same here for me. Sometimes it's flat out....other times there are tumble weeds blowing through my work area. Looking forward to reading about success with the Samsung tv !
          Best Regards

          Likes(1)Dislikes(0)
          • Robert Calk

            October 13, 2015 at 4:42 am

            Hi Albert,
            I'm just a hobbyist anyway. I just do electronix for the fun of it, and also to save myself, family, and friends some money when I can.

            Likes(0)Dislikes(0)
          • Robert Calk

            October 13, 2015 at 4:44 am

            Sorry Anthony, I called you Albert by mistake.

            Likes(0)Dislikes(0)
            • Albert van Bemmelen

              October 14, 2015 at 3:17 pm

              Don't worry Robert. Our names both end on Bert. And my fathers name is also Bert from Dutch name Gijsbertus. It seems we do keep Jestine busy with redigating our typoos.

              Likes(0)Dislikes(0)
  4. Mustafa

    October 9, 2015 at 7:05 pm

    hello,

    I think it's great and very informative .
    I want to thank you for the Happy and Holy .
    good luck.

    Likes(1)Dislikes(0)
    • Gerald

      October 9, 2015 at 9:26 pm

      Thanks for your appreciation and comment Mustafa.

      Likes(0)Dislikes(0)
  5. Pepper

    October 9, 2015 at 9:05 pm

    Excellent presentation Mr.Musy!
    To identify the `type' diode you have;
    -Germanium forward bias = .2v to .3v.
    -Silicone forward bias = .6v to .7v.
    -Schottky forward bias = .86v.
    Mult-meters with a `diode' test function will often display the above voltages directly.

    Likes(1)Dislikes(0)
    • Florian Ion

      October 10, 2015 at 12:16 am

      ForSchottky diodes Vf is not 0.86V, maybe half. Please check it.

      Likes(2)Dislikes(0)
      • Robert Calk

        October 13, 2015 at 4:50 am

        And are usually around .2V - .4V.

        Likes(3)Dislikes(0)
    • Gerald

      October 10, 2015 at 11:03 am

      Hi Pepper, thanks for your feedback.
      Cheers,
      Gerald

      Likes(0)Dislikes(0)
  6. Humberto

    October 9, 2015 at 10:48 pm

    Good explanations, as usual in your articles. Congratulations Professor.

    Likes(0)Dislikes(0)
    • Gerald

      October 10, 2015 at 4:59 pm

      Thanks Humberto 🙂

      Likes(0)Dislikes(0)
  7. Anthony

    October 10, 2015 at 3:39 am

    Thank you for this very good article Gerald. I will print it out and keep it for reference. Thank you very much for taking
    the time to share it with us !
    Kind Regards

    Likes(0)Dislikes(0)
    • Gerald

      October 10, 2015 at 5:00 pm

      Thanks for your support Anthony.

      Likes(0)Dislikes(0)
  8. Mark

    October 11, 2015 at 2:55 pm

    Hey Gerald,
    Well explained as usual. I enjoy the details as to why things work and the ratings they must work within.
    It is easy to get it wrong in electronics and lose the 'magic smoke'!
    It's the way we all learn, especially us enthusiasts.
    Keep us informed and keep up with the good work!

    Likes(0)Dislikes(0)
    • Gerald

      October 12, 2015 at 9:14 am

      Hi Mark, thanks for your support.
      I agree with your comment and this is why they said that engineers are fundamentally honest… Because they cannot cheat, they have no choice. Connect a wire to the wrong terminal and it will not work or it will go into smoke. A mechanical part with the wrong dimensions will not fit and a bridge with the wrong supports size will collapse 🙂
      Cheers,
      Gerald

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      • Robert Calk

        October 12, 2015 at 1:58 pm

        That's true, but usually when we fail or are having a hard time is when we learn the most.

        Likes(1)Dislikes(0)
  9. Philip P George

    October 12, 2015 at 9:07 pm

    Very nicely explained.Thank you very much.

    Likes(0)Dislikes(0)
  10. Paris Azis

    October 14, 2015 at 1:13 am

    Hello Gerald

    Excellent presentation. Allow me please to add only a detail. The LEDs of 3mm in diameter have a maximum current of 5mA, while those of 5mm diameter have a maximum current of 20mA.
    Personally when I build a project I always have the LEDs working with the half of their maximum values in order to ensure their longevity.

    Best Regards

    Likes(0)Dislikes(0)
  11. Albert van Bemmelen

    October 14, 2015 at 3:22 pm

    Hi Paris. Are you sure? I never bothered to limit to 5 mA. See for instance:

    https://www.sparkfun.com/products/533

    Cheers, Albert.

    Likes(0)Dislikes(0)
    • Paris Azis

      October 14, 2015 at 8:49 pm

      This one you refer to Albert is of high luminosity and perhaps it can with stand so much current.
      I am talking about the older, standard types. It seems that they differ even in their forward voltage drops. The ones I have in mind are of the order of 1,6V.
      Apart from that and during repairs I always see what resistors the manufacturers use to drive LEDs, this being an additional proof about the topic.
      Gerald is quite right saying that even if you drive them with the half or even less current they optically give the sense that they glow in the same intensity.
      Anyway I never apply more than 3 mA on standard 3mm types.

      Greetings!

      Likes(0)Dislikes(0)
    • Robert Calk

      October 15, 2015 at 2:46 pm

      That's another reason why I love my Peak Atlas Zen50, zener tester - it has test currents of 2, 5, 10, and 15mA; which is perfect for LED's. I can test an LED at the various currents and see where the slope resistance(Rslope), sometimes called the dynamic resistance or differential resistance, is the lowest for a particular LED. One of the 5mm Red LED's, like the one I used in my low voltage polarity checker article, has the lowest slope resistance(11ohms) and a forward voltage(Vf) of 1.86V at a current of 15mA. At a current of 2mA, it has a slope resistance of(25ohms) with a Vf of 1.66V.
      So according to my Zen50, the optimal current for this LED seems to be about 10mA.
      But I'm no scientist, so if anyone knows more and would like to share their knowledge with us I would like to read your comments.

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      • Robert Calk

        October 15, 2015 at 2:49 pm

        Oops, I meant an optimal current of 15ma, not 10mA. Sorry guys.

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        • Albert van Bemmelen

          October 18, 2015 at 2:31 am

          I am glad you still like your Peak Atlas as much Robert. But I myself do not use such a quite expensive tester that even needs a special 12V battery just for testing simpel components like Leds. But I understand the things you like about it. But paying far over $107 US Dollar including Shipping is too much for my taste.

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          • Robert Calk

            October 18, 2015 at 6:17 pm

            Hi Albert,
            What you have heard is not true! The Zen50 uses only 1 AAA alkaline battery, and you can get it at the main website in the UK for only 39 pounds. They are made in England. Here is their website: http://www.peakelec.co.uk/acatalog/jz_instruments.html
            I mainly bought it for Zener diodes, but it is also great for LED's.

            Likes(1)Dislikes(0)
            • Albert van Bemmelen

              October 20, 2015 at 3:12 pm

              Thanks Robert. My friend with his ICT/repair shop had a Transistortester from the same Manufacturer and that one had a 12V battery that was empty after about a year of hardly using. And as far I know it had an electronic automatic off switch, instead of a normal off switch. And as you probably know that forces any user to remove the battery afterwards before putting the tester aside for a longer period. I will have a look at the link you gave and see what the price of the Zen50 will be. Thanks!

              Likes(0)Dislikes(0)
              • Albert van Bemmelen

                October 20, 2015 at 4:13 pm

                I've checked Robert. Since England is in the European community it is much cheaper than the Ebay prices when those Zen50's are coming from the USA. Those cost including shipping to Europe much more. But they still cost about 49.44 British Pound when directly ordered from the UK, which is about 68 Euros. And since the tester only tests Zeners up to 50V and diodes like leds which are easy to test, I think it is still a very expensive buy. You see for the money it costs I am able to buy almost 8 cheap but good Digital universal Meters or any other Universal Digital tester that can do much more. And I've got some very good ones already! Including portable digital testers (operating on one single AAA mini penlight Battery also!) that can test Zeners too including all TTL and CMOS ICs and LEDs etc. And that tester also tests led displays , opamps, optocouplers and is so small you could lose it in your pocket. All China made of course and one third of the cost of any European build device. That probably also was manufactured in China?That same qualification undoubtedly you can say for instance of all Arduino Boards that are way cheaper ordered from China. With the only difference on those boards being another Serial to USB chip (The CH340G) which they in Europe say sometimes could cause problems, but worked okay for me ! The only thing coming from China that could be worse compared to European build devices I think could only be the often lesser quality of the plastic used in the housing of the electronic devices. And the way in which they probably wouldn't survive any fall to the ground. Then I should probably buy an expensive Fluke Digital meter that is made to survive rough industrial envirements. But if you handle the cheap China meters with care, the plastic parts will survive long enough at home.

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                • Robert Calk

                  October 20, 2015 at 6:13 pm

                  It is the only meter I have found at that price that will give the slope resistance. It also tests a lot more than zeners & LEDs.
                  I would love to see this little meter of yours that is so cheap and will check everything.
                  I also bought the great little transistor tester DY-294 that will test zeners up to many hundreds of volts, but it doesn't give the slope resistance, which I think is very nice to see for zeners and also for the optimum current for an LED. I can check most 2 and 3 pin components, and optocouplers with my analog VOM, but no Rslope.
                  If you have a cheap meter that will give the Rslope, let everyone know the name of it so that people that cannot afford a Zen50 can buy one of those. I am only trying to help people.

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                  • Albert van Bemmelen

                    October 20, 2015 at 11:49 pm

                    Hi Robert. I think I never needed the Slope resistance before of a Zener Diode or any other component. And I probably haven't got any meter that gives me those values either. But that doesn't matter at all! I know that components are never ideal but I can live with that without any problem whatsoever. But I can imagine that you need more information when you want to make an electronic device that works on batteries and should be working almost close to perfect. But when is that ever going to happen? And the slope value probably can be easily calculated by measuring both Current and Voltage. But I never need the Slope resistance. I can easily do anything without knowing it.

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                    • Albert van Bemmelen

                      October 21, 2015 at 4:28 am

                      By-the-way Robert here are the links to my universal IC/component/display/led testers I bought on Ebay:

                      http://www.ebay.com/itm/Transistor-Tester-Detect-IC-Meter-Maintenance-Digital-led-Tester-MOS-PNP-NPN-/262080543919?hash=item3d0537bcaf

                      http://www.ebay.com/itm/Multi-functional-IC-74-CD4000-series-IC-NO-checker-LED-Tester-Detector-USB-/321078818488?hash=item4ac1c9f6b8

                      http://www.ebay.com/itm/2014-Mega328-Transistor-Tester-Diode-Triode-Capacitance-ESR-Meter-MOS-PNP-NPN-/111350714802?hash=item19ed0511b2

                      I have some more Digital Testers but they are not universal and for instance only for ESR or Capacitance Tests. (These were also mentioned on Jestine's repair site). Links are on Ebay:
                      http://www.ebay.com/itm/281165912260?_trksid=p2057872.m2749.l2649&ssPageName=STRK%3AMEBIDX%3AIT

                      and

                      http://www.ebay.com/itm/MESR-100-ESR-Low-Ohm-In-Circuit-Capacitor-Meter-SMD-Clip-Probe-/330951990098?hash=item4d0e469b52

                      Cheers, Albert.

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  12. Albert van Bemmelen

    October 21, 2015 at 4:35 am

    PS: the second link shown is the USB powered version. But my mini tester only uses a mini penlight battery without the USB connection cable for powering version.

    Likes(0)Dislikes(0)
  13. Robert Calk

    October 21, 2015 at 9:00 am

    Thanks Albert. Those look like good meters.
    I have the M6013 myself. Maybe some viewers
    can benefit from your list of meters.

    Likes(1)Dislikes(0)
  14. Robert Calk

    October 22, 2015 at 3:24 am

    To Albert and anyone that is interested, I found this
    on a website that gives some insight into slope resistance,
    (or dynamic/ differential resistance).
    http://electronics.stackexchange.com/questions/97883/
    resistance-of-a-semiconductor-diode

    Likes(0)Dislikes(0)
    • Albert van Bemmelen

      October 22, 2015 at 3:34 pm

      Thanks Robert, I will have a look. And see if it does make me decide to also buy a Zen50.

      Likes(0)Dislikes(0)
      • Albert van Bemmelen

        October 22, 2015 at 4:09 pm

        If I understand it correctly does your Zen50 tester give the DC or Static Resistance. Which is a momentary Resistance measured at a certain DC forward current value at a certain corresponding DC Voltage over a diode, led or an avalanche breakthrough conducting zenerdiode. But given that no component is ideal and even one peticular component produced in large quantities has a deviation often catagorized in Datasheet values between Max, Typical and Min values, they all do work. And it only is important to know what limits are given in order to keep your component healthy. And knowing the Static Resistance doesn't really help you in any way, I think.

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  15. Robert Calk

    October 22, 2015 at 10:36 pm

    Hi Albert,
    I'm not sure - I'm learning myself. But what we do know
    is that resistance = heat. So it seems to me that a diode,
    especially a LED, that has a higher slope resistance will
    also have higher internal heat. How much that really matters,
    I'm not sure. I was hoping that someone who has formal
    training in these matters would educate us.
    I'm not a Zen50 salesman, but until I bought one, I had
    never even heard of slope resistance, which is also called
    dynamic or differential resistance. That's another problem:
    slope resistance is called by so many different names that
    it is hard to find information about it. But of course, an
    LED would be more susceptible to internal heat than a zener
    or normal diode would be.

    Likes(0)Dislikes(0)
    • Albert van Bemmelen

      October 23, 2015 at 8:44 pm

      Hi Robert, I'm no expert either but from the Link you gave about the slope resistance information website I understood that it all depends how you take the information from the current / voltage curve of your component. And because the diode curve isn't lineair its steepness or vertical slope increases non-lineair with an increasing momentary Forward voltage value. If you only measure on one momentary point on that curve you measure the DC or Static Resistance. At a certain forward I value and V value. Suppose I is 1mA.
      And if you instead of one point use a triangle to measure its steepness over a larger area of the rising curve, beginning in the exact same momentary point you are able to detect the average rising value given out delta I and delta V. Whereas both deltas represent the amount in which I and V have changed from beginning point to the last point on the curve. And that they call that the Dynamic Resistance. And there is another way of measuring and also by using a triangle. So it all depends how many values you take on that curve.

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  16. Robert Calk

    October 23, 2015 at 10:14 pm

    The Zen50 takes 3 measurements to find the slope resistance.
    You can read the user manual at their website. I would
    imagine that a LED operating with much higher Rslope will
    burnout faster than one with a lower Rslope. I guess I will
    build 2 circuits on a breadboard with the same LED's that are
    also from the same batch. Then operate one at a current with
    high Rslope(about 20ohms), and the other LED at a current that
    has real low Rslope(about 1ohm), 24 hours a day. Then I'll see
    which one burns out first. If a LED having high Rslope really
    matters, there should be a big difference in their longevity.

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  17. Robert Calk

    October 23, 2015 at 10:16 pm

    P.S. For some reason this article is clipping the comments
    short. That is why I'm making the sentences shorter.

    Likes(1)Dislikes(0)
  18. Albert van Bemmelen

    October 25, 2015 at 2:58 pm

    Yes Robert, I noticed that too.
    I previously also made my sentences shorter.
    But I probably already wrote too much lenghtly sentences. Haha.

    Likes(1)Dislikes(0)
  19. Seeran Kunendran

    March 14, 2016 at 1:41 am

    Can someone help me to explain why at 20 to 30mA the line starts to curve for the luminous intensity Vs Forward current.

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