I have the following circuit, where I put R52 = R53 = 2700 Ohms :    Triggering levels are of 1V and 2V approximately according to my computations, that is okay according to the following figure showing input in green and output in blue :    But what I find really strange is that the maximum voltage output is around 3.3V and not at 5V. How would you explain that ? And last detail : how would you explain that the output is not exactly at 0V when the input is high?  Thank you very much for your help.
First Question for me.  I have benefited from other answers here but have not fully resolved my problem.  Here's my problem...  The LM311 Comparator output does not drive the N channel MOSFET fully on.  The LM311 has a 110mv ref voltage on the inverting input. The non-inverting input is driven by an opto-isolator output. The Opto-isolator is driven by 1 of 4, AC 60Hz voltages.  &lt;1VAC, 9VAC, 55VAC and 115VAC.  The goal of the design is to have the FET fully turn on the 12VDC fan when there is appreciable AC voltage.  So fan fully On for the 9, 55, and 115VAC voltages.  It seems it should work because I measure voltages on the non inverting input of 1.6, 2.2 and 3VDC respectively for the 3 appreciable AC voltages.  And my ref voltage on the inverting input is 110mv.  So it "almost" works because the fan is off at the &lt;1VAC, but not fully "On" for the other AC voltages.  I believe this is because Vgs is 167mv, 6.1V, 7.7V and 9.9 Volts for the 4 AC voltages listed above.  And the fan is only getting 7, 8 and 10VDC instead of a desired 12VDC. Would really like to be able to fully turn this FET all the way on.  So Close!  Any input or guidance is appreciated.  Ps-Things I think I've done right? Flyback diode across the fan. Putting N channel FET to switch to ground on low side of fan. LM311 has Open collector output using correctly?  PSS-I realize that the pinouts for the LM311 are not right in my schematic.  I have them right in my protoboard circuit.  Its a single device.  Pin 2 is noninveritng and pin 3 in Inverting  Thanks Again.      The suggested duplicate question and answer doesn't help for the following reasons: Both diagram and schematic are"No file found" making it pretty difficult to follow the answers. I am not using any positive feedback in my circuit as I don't think I need one. I have a simple pull up resistor to my 12V supply, not a voltage divider to the power supply as is mentioned in the answer. Thanks.  Just for the record I wanted to post a more accurate schematic and thanks for the response on using a Cap to hold up the opto isolator output. I actually have a full wave input to the phototransistor but I'm sure the cap will help anyway. To answer the last question, the Pin 7 comparator output has a pullup resistor to 12v. The issue is still that Vgs is only 10v when the comparator has 3v on pin 2 and 110mv on pin 3. I would have expected the LM311 output to go much closer to 12v (Vcc) with those inputs. The intent is for the FET to go completely on for pin 2 voltage > pin 3.
How can I evaluate $$\sum_{n=1}^\infty\frac{2n}{3^{n+1}}$$? I know the answer thanks to , but I'm more concerned with how I can derive that answer. It cites tests to prove that it is convergent, but my class has never learned these before. So I feel that there must be a simpler method.  In general, how can I evaluate $$\sum_{n=0}^\infty (n+1)x^n?$$ Why are the laws of thermodynamics "supreme among the laws of Nature"? Eddington wrote     The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations — then so much the worse for Maxwell's equations. If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.   and Einstein wrote     [classical thermodynamics] is the only physical theory of universal content which I am convinced will never be overthrown, within the framework of applicability of its basic concepts.   Why did they say that? Is it a very deep insight they had, or is it something one can be convinced of quite easily? Or even, is it trivial? Edited vs emitted - why one t vs two t's Why does "edited" have one "t" and  and "emitted" has two? "Edit" and "emit" are so similar in spelling and pronunciation.  I keep wanting to type "editted" for some reason. As I found solutions on making site-to-site VPN between Azure and AWS using a software VPN server, I'm asking myself if it's possible to connect the VPN gateways (Azure VNET / AWS VPC) directly.  Is there a limitation that forbids it ? Bezout's identity in $F[x]$ Let $F$ be a field and $F[x]$ a polynomial ring. Let $p(x)$ be an irreducible polynomial.  Show that $\gcd(p(x),q(x)) = 1\Longrightarrow \exists r(x),s(x)$ such that $r(x)p(x)+s(x)q(x) = 1$.  I know the proof for Bezout's identity for , but this proof uses the notion of absolute value, which cannot be applied to a polynomial ring.   I am thinking about a way to prove the statement: Use the Euclidean algorithm to compute $\gcd(p(x),q(x))$ and show that the result is $1$, and somehow go backwards to obtain $r(x)p(x)+s(x)q(x) = 1$, but it is a bit messy, and I'm not yet able to see it completely.  Please offer some help. If you have some other methods, that would be great, too. Difference between @RemoteAction annotation and ? jquery's append not working with svg element? Why does speed of light have to be constant? My question is not about why speed of light has a particular constant value which has been sufficiently addressed in other questions on SE already. I want to know whether the fact that speed of light has to be constant is a consequence of other fundamental laws of Universe, or is it just a fundamental law itself.  My motivation for asking this question is thinking about Special Theory of Relativity. One way of understanding why time dilation and length contraction happen is to look at it from the perspective of constancy of speed of light. Alice who is on the moving source of light and Bob, a fixed observer see the speed of light as constant. In order for Alice to see the speed of light as a constant value, time slows down and length expands (in forward direction) thus keeping the speed constant.   In the  I'm doing, the Professor tells that this constancy of speed of light could be more generally referred to as, "Principle of wave constancy". That is, the speed of any wave is a property of the medium (and thus it remains constant). So, the speed of a wave in water, for example, remains constant even if the source of the waves (say a paddle keeps moving). Frequency and wavelength may change but the speed remains constant. In a similar fashion, light is an electromagnetic wave and thus its speed is constant. And the constant speed is defined by the medium (which happens to be vaccum i.e., no medium for light).   My questions are twofold now -    Is the above reasoning correct to explain why speed of light is constant? (i.e., thinking of it as constancy of any wave in general) Theoretically, could there be other waves that could travel through vaccum at a different speed? If yes, time dilation and length contraction will have to be different.   I'd appreciate it if the answer is kept non-technical (essential math is okay). More importantly, I request you to try and explain without using General Theory of Relativity. Because I'm thinking how the scientific understanding by 1905 had already knew that speed of light has to be constant. How to install the previous version of a .deb package and pin it? I am trying to install the latest version of subversion on Sid, and because it has a bug I receive a warning and I abort the installation. How do I get to locate the previous version version, install it and pin until the bug is resolved?  root@server01:~# apt-get install subversion   Reading package lists... Done                                                                                                                                                                                  Building dependency tree                                                                                                                                                                                       Reading state information... Done                                                                                                                                                                              Suggested packages:                                                                                                                                                                                              db5.3-util subversion-tools                                                                                                                                                                                  The following NEW packages will be installed:                                                                                                                                                                    subversion                                                                                                                                                                                                   0 upgraded, 1 newly installed, 0 to remove and 205 not upgraded.                                                                                                                                               Need to get 0 B/981 kB of archives.                                                                                                                                                                            After this operation, 4,844 kB of additional disk space will be used.                                                                                                                                          Retrieving bug reports... Done                                                                                                                                                                                 Parsing Found/Fixed information... Done                                                                                                                                                                        critical bugs of subversion (-&gt; 1.9.2-2) &lt;Outstanding&gt;                                                                                                                                                          b1 - #803725 - subversion: dump-load of a repository modifies verbose log output: M line lost serious bugs of subversion (-&gt; 1.9.2-2) &lt;Outstanding&gt;  b2 - #803589 - FTBFS with ruby2.2 (only) Summary:  subversion(2 bugs) Are you sure you want to install/upgrade the above packages? [Y/n/?/...] n ********************************************************************** ****** Exiting with an error in order to stop the installation. ****** ********************************************************************** E: Sub-process /usr/sbin/apt-listbugs apt returned an error code (10) E: Failure running script /usr/sbin/apt-listbugs apt Implements vs extends: When to use? What's the difference? I'm hoping someone can give me a nudge in the right direction...     Let $F$ be a finite field, and let $f(x)$ be a nonconstant polynomial whose derivative is the zero polynomial.  Prove that $f$ cannot be irreducible over $F$.   I've got that every root of $f$ is a multiple root and that for $F=\mathbb{F}_{p^r}$, the exponent of every term of $f$ is a multiple of $p$. Showing that ${\rm E}[X]=\sum_{k=0}^\infty P(X>k)$ for a discrete random variable Let $X$ be a discrete random variable whose range is $0,1,2,3,\ldots$. Prove that $$ {\rm E}[X]=\sum_{k=0}^\infty P(X&gt;k). $$  How to prove this? I tried a bit but unable to post due to formatting issue. Can anyone help? override parent theme configuration in child functions.php Can Yahoo! Messenger be used with Ubuntu? I recently re-watched Contact for the first time since my childhood, and while I thoroughly enjoyed it, I realized that there was something I'd never understood: why couldn't they corroborate Ellie's account of her journey?  As far as I could tell, the pod fell harmlessly through the machine.  That is, it didn't break anything, and the machine wasn't destroyed.  I don't recall any dialogue about circuits being fried or the system shutting down, so presumably it wouldn't be hard to simply hoist the pod up and go again.  I imagine the energy draw was substantial on the local Japanese power grid, but given the amount of effort and money already invested in the machine, surely "Round 2" wasn't out of the question?  I mean, they almost certainly expected that this machine would get more than one good use out of it, anyway!  So given Ellie's vehement insistence that the machine had worked, the public nature of the controversy surrounding her testimony, and the government's (secret) findings that her device had recorded 18 hours of static, why wasn't it the obvious choice to have someone else suiting up the next day, ready to drop through the machine and corroborate her story? Lately I've been seeing this cookie popup that blocks a lot of the screen.  When I try to do the &quot;manage cookies&quot; thing, all it shows me are several categories, with a green oval containing a black circle to the right of each.  Clicking on that oval makes it disappear.  Clicking on the same spot again makes it reappear.  But I see no indication as to which state is off or on. So how can I make this popup go away, never to bother me again?  Or failing that, could you at least provide some indication as to what those buttons do?  Like maybe simple text saying &quot;Off&quot; or &quot;On&quot;? What does A a() mean? What will be the one's digit of the remainder in: $\left|5555^{2222} + 2222^{5555}\right|\div 7=?$ Counting traversed arcs on routes to write attributes using ArcGIS for Desktop? I have number of persons located on a road network and I have calculated their shortest distance to a particular location.  From the routes output created from Closest Facility can I   break the routes down into the individual arcs traversed by each person? assign each arc a count attribute indicating the number of individuals who use that arc to get to their destination?   I am using Network Analyst in ArcGIS 10.2 for Desktop. How to discard unsaved changes to a view when editing it leads to a WSOD?