If I have 4 identical* LEDs wired in parallel to a single resistor so that the overall current available is 30 mA, do I still run the risk of premature burnout? The LEDs peak forward current is 30 mA.   *I know that LEDs from the same package may still have slight differences  I thoroughly read through the answers here -  - but it seems like the assumption would be that one would arrange a circuit so that the available current equals the total draw of the 4 LEDs, in my case 80 mA. The problem then would be that some would draw more than the peak. But, if I'm limiting the avaialble current to 30mA, is there still an issue? That would mean that ideally 7.5mA would be supplied to each LED. Obviously, based on the answer in the aforementioned link, it would not likely be even, but it shouldn't get to "dangerous levels".   Follow-up: Based on the volt/amperage curve, it looks like I'd be seeing a ~0.1V drop. Will this significantly affect the brightness?    Still pretty new to all this so my apologies for any incorrect terminology and faulty logic!
I'm trying to wire up 6 RGB LEDs in parallel, all controlled from a single source (well, three sources, one for each colour). The LEDs came supplied with resistors to limit the current of 270 Ohm for a 5v supply.  The problem is, 6 LEDs x 3 colours = 18 resistors, which is a lot, and means I need a much bigger board and a lot more soldering.  So, can I instead wire the LEDs in parallel with each other, with a single resistor protecting all six? (3 resistors in total, one for each colour). How do I calculate the value of that resistor?  More details:  The LEDs are being driven from a  to supply a bit of current, which is in turn controlled by a Netduino providing a PWM signal on the three channels.  . If I've correctly understood the data sheet they want 20mA of current, and forward voltages of 2, 3, 3 volts (for R,G and B respectively?). The supplied resistors were all 270 Ohm, so the channels may not be balanced quite right.  For extra credit: I'm only using 3 of the transistors in my driver chip, which has 8 in total. could I wire the PWM from the netduino to a second trio of transistors, and split the LEDs into two groups of three? Is it worth the effort?  PS I don't have any diagramming tools to hand, but I can provide a diagram (drawn in paint) if it would help clarify my question. (see also )
Which past tense of "to light" should I use here? I know that there are two ways to form the past tense of to light (i.e. lit/lighted). Which one is appropriate for the sentence below?     His thoughts lighted our way.   or     His thoughts lit our way. How can I repeat the header but not the caption with longtable? I am trying to set up a longtable where the header is repeated on every new page but the caption only appears once at the top of the page.  The table is defined as follows:  \begin{longtable}{|l|l|l|} \caption{the table caption} \label{tab:11swpkg}\\ \hline \rowcolor{gray} HeaderCol1 &amp; HeaderCol2 &amp; HeaderCol3\endhead     \hline\hline Item11 &amp; Item12 &amp; Item13 \\ \hline Item21 &amp; Item22 &amp; Item23 \\ \hline Item31 &amp; Item32 &amp; Item33 \\ \hline \end{longtable}   This nearly works because the header is indeed repeated after a page break but so is the caption. How can I get rid of the caption after a page break? I'm trying to purchase a domain name that was registered and apparently already expired. This is its status:  Status: clientHold http://www.icann.org/epp#clientHold Status: clientTransferProhibited http://www.icann.org/epp#clientTransferProhibited Status: redemptionPeriod http://www.icann.org/epp#redemptionPeriod Updated Date: 14-oct-2015 Creation Date: 01-sep-2014 Expiration Date: 01-sep-2015   From what I'm seeing from ICANN policies, it should already be available to be registered by third parties, but maybe I'm missing something. When will it become available for me to register it? This came up in  , but I can't see good documentation or examples that explain how the feature works. Prove using induction that from a set of $n+1$ numbers from $\{1,2,..2n\}$, at least one number will evenly divide another. Given a set of $n+1$ numbers out of the first $2n$ natural numbers, $\{1,2,\ldots,2n\}$, prove that there are two numbers in the set, one of which divides the other.  I can't tell if I'm reducing the problem in the right way.  Would it be something like:  Induction Hypothesis: A set of $n+1$ numbers from the first $2n$ natural numbers contains two numbers, one of which evenly divides the other.  Base Case: $n=1$, $\{1,2\}$, 2 is divisible by 1.  Consider a set of $n+2$ numbers, $A$, from the first $2n+2$ natural numbers. There are three cases:   Each number in $A$ is less than or equal to $2n$.  The proof follows from the induction hypothesis. One number in $A$ is greater than $2n$.  The remaining set of $n+1$ numbers must each be less than or equal to $2n$.  The proof follows from the induction hypothesis. $A$ contains both $2n+1$ and $2n+2$. I'm not sure how to solve this case.   I'm working through Udi Manber's Introduction To Algorithms: A Creative Approach for personal development, so in keeping with the spirit of the book, I'm trying to use induction.  Without induction, the question is identical to Singular or plural verb after parenthetical material containing a conjunction? I would tend to say     Sara (and all of us) have a lot to think about now.   ...but it occurs to me that if I remove the parenthetical it's clearly incorrect. Is it proper to say     Sara (and all of us) has a lot to think about now.   ...that sounds really strange to my ear.  Also, does it change the rules in any way if I use an em dash, e.g.     Sara–and all of us–have a lot to think about now. What exactly does Perl's "bless" do? I understand one uses the "bless" keyword in Perl inside a class's "new" method:  sub new {     my $self = bless { };     return $self; }       But what exactly is "bless" doing to that hash reference ? On Ubuntu 18.04, I have connected my laptop to an external display and I am able to set the external display as primary and external display only mode. But when I turn on my laptop or log out from my session the display login screen is displayed only on my(internal) laptop screen. But once I login the display switches to external only and my laptop screen turns off as expected. Is there a way I can make the login screen appear only on the external screen on bootup or on logout as in 16.04? Also the login screen does not follow my cursor as in 16.04. How to install Ubuntu on a laptop with Windows 10 I want to install Ubuntu and remove Windows 10 , but when you restart the PC does not read the Ubuntu installer that is on a bootable USB. Adding more than 15 digits in Excel $x^4 + y^4 = z^2$ $x, y, z \in \mathbb{N}$,    $\gcd(x, y) = 1$  prove that $x^4 + y^4 = z^2$ has no solutions.  It is true even without $\gcd(x, y) = 1$, but it is easy to see that  $\gcd(x, y)$ must be $1$ Unicode applies the convention of using a  as signature at the beginning of a text stream, identifying the encoding used within it. The following three bytes at the beginning of a file: EF BB BF, identifies this file as a UTF8 file. Vi and most text editors gracefully ignore this signature. Open office does that as well, but it adds this signature at the beginning.  Now, if I open a TeX file with OpenOffic.org, and I do that quite a lot (for mixed directionality editing), the signature is added, and baffles LaTeX, which produces an error message such as:   ! LaTeX Error: Missing \begin{document}.   See the LaTeX manual or LaTeX Companion for explanation.  Type  H &lt;return&gt;  for immediate help.  ...                                                l.1   ��\documentclass{article}   whereas a simple dump of the file does not show the problem. Is there a way to eliminate this problem, while staying in the realm of latex? "How it works?" vs. "How does it work?" What is the difference between:        "How it works?"      and        "How does it work?" It is well known from Noether's Theorem how from continuous symmetries in the Lagrangian one gets a conserved charge which corresponds to linear momentum, angular momentum for translational and rotational symmetries and others.  Is there any elementary argument for why linear or angular momentum specifically (and not other conserved quantities) are conserved which does not require knowledge of Lagrangians? By elementary I mean, "if this is not so, then this unreasonable thing occurs".   Of course, we can say "if we want our laws to be the same at a different point in space then linear conservation must be conserved", but can we derive mathematically the expression for the conserved quantity without using the Lagrangian?  I want to explain to a friend why they are conserved but he doesn't have the background to understand the Lagrangian formalism. I just came across this code and a few Google searches turn up no explanation of this mysterious (to me) syntax.  Hashtable^ tempHash = gcnew Hashtable(iterators_);  IDictionaryEnumerator^ enumerator = tempHash-&gt;GetEnumerator();   What the heck does the caret mean? (The gcnew is also new to me, and I asked about that .) Are there any add-ons that will cause a browser to automatically refresh a page when a particular file changes on disk? What is the best way to close an ASPX page from the code-behind?    I have a button event handler that I want to close the page after the user has clicked an ASP.NET button on the page.  I have tried to programmatically add a JavaScript method that contains a window.close() command to the OnClientClick event to close the page but it does not work.  The button is also a asp:AsyncPostBoskTrigger for an AJAX Update Panel.  The application uses .NET Framework 3.5. If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$ Travel in the Schengen area after my residence card was lost or stolen I have already booked my flight from Italy to the Netherlands through Ryanair. I'm staying in Italy legally and have a carta di soggiorno. However, after booking my flight, my wallet was stolen, which contains all my IDs except my passport. I filed a police report, and I'm trying to get a new residence card. However, I need to go to the Netherlands ASAP. Will Ryanair accept the police report and receipt of getting a new residence card from the post office?  UPDATE (17.07.2014)  Thanks for helping me out. BTW it's OK now. I went to our local CISL here in Florence, Italy, where they process your envelope for renewing your permesso di soggornio or carta di soggiorno (residence permit for foreigners) to be submitted to the post office. That's where you pay and get your postal receipt, and they make an appointment for you at the questura. Anyway, long story short, they processed a application for IMPROVISED residence permit which is good for 30 days to travel within the Schengen area, so all I have to do is go to the questura, bring my travel booking, the police report and copy of my passport. Now I can travel, and it's my first time to fly with Ryanair because I always use Transavia to go to Holland. =) Hope this helps for future persons who will have the same issue with lost or stolen residence permits...Just wish me luck that the questura will process my improvised residence permit immediately. Characterising reals with terminating decimal expansions Show that a number has a terminating decimal expansion if and only if, it is rational and when in lowest terms, its denominator is coprime to all primes other than $2$ and $5$.   This is an unsolved question in my lecture notes. I can only seem to prove the converse direction for this. Would appreciate a solution for the other direction.     For converse direction:   Let the number, in lowest terms, be given by $\frac{l}{m}$ where $m = 2^ \alpha 5^\beta$, for some positive integers, $\alpha$ and $\beta$.    If $\alpha &gt; \beta$, let $k = 5^{(\alpha-\beta)}$. If $\alpha &lt; \beta$, let $k = 2^{(\beta-\alpha)}$.   Then $\frac{l}{m} = \frac{kl}{k2^\alpha5^\beta}=\frac{kl}{10^q}$ where $q = \max(\alpha,\beta)$.   Hence $\frac{l}{m}$ is a terminating decimal.