I read somewhere that the addition of R2 provides the DC return to ground however this would reduce the overall input impedance of the op-amp. Input impedance must be high for an op-amp. How to solve this problem?
In the case of a non-inverting amplifier, if I DC couple the input signal with a capacitor only, \$C_1\$ (i.e. no resistor to ground), sources (as well as an experiment in the lab) show me that the op amp input will be saturated as the input bias current deposits charges on the terminal without having a return path to ground. This is solved by using connecting a resistor (\$R_1\$, as shown in the image below) to ground to create the return path. [The image is reproduced from an answer by "Neil_UK" on one of my previous questions, thanks Neil!]    My questions:   1) How is the input bias current able to continuously deposit charges and saturate the input if I don't use the resistor? The resistor should not allow the DC bias current through, so where is this current flowing from/into?  2) Why is this not a problem for the feedback path to the "-" terminal? There is no resistor to ground in that case, and capacitor \$C_2\$ seems to be causing no issues. The PDFs I've been reading suggest that the feedback behaves similar to when I have a resistor to ground by acting as the return path, how is this?
How to add horizontal cylinder at end of cube Extracting usernames from the /etc/passwd file Calculation of $\int_0^{\pi} \frac{\sin^2 x}{a^2+b^2-2ab \cos x}\mathrm dx$ Calculate the definite integral      $$ I=\int_0^{\pi} \frac{\sin^2 x}{a^2+b^2-2ab \cos x}\;\mathrm dx $$      given that $a&gt;b&gt;0$.   My Attempt:  If we replace $x$ by $C$, then  $$ I = \int_{0}^{\pi}\frac{\sin^2 C}{a^2+b^2-2ab\cos C}\;\mathrm dC $$  Now we can use the Cosine Formula ($A+B+C=\pi$). Applying the formula gives  $$ \begin{align} \cos C &amp;= \frac{a^2+b^2-c^2}{2ab}\\ a^2+b^2-2ab\cos C &amp;= c^2 \end{align} $$  From here we can use the formula $\dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c}$ to transform the integral to  $$ \begin{align} I &amp;= \int_{0}^{\pi}\frac{\sin^2 C}{c^2}\;\mathrm dC\\ &amp;= \int_{0}^{\pi}\frac{\sin^2A}{a^2}\;\mathrm dC\\ &amp;= \int_{0}^{\pi}\frac{\sin^2 B}{b^2}\;\mathrm dC \end{align} $$  Is my process right? If not, how can I calculate the above integral? I often hear people saying that "I am" is the shortest sentence in the English language.  I know that there are also discussions about sentences using the imperative mood such as "Go." that would be shorter, but my question is this:  Why would we (the people saying "I am" is a full sentence) not accept "I'm" as a complete sentence?  Is there some unwritten rule about contractions that says "I'm" wouldn't be correct? What temperature is achieved in focus point by 5000 flat 1x1cm mirrors onto a satellite dish? There is this  ("R5800 Solar Death Ray") where teenager built a 5000 mirror device which concetrates the solar rays which is showing the potency of the mosaic method of concentrating sunlight using elliptical dish. It can fire the wood, boil the water in seconds, melt an aluminum, glass or even burn the whole in concrere or rock.  What is the approximate maximum temperature (could be a range) is achieved by this mirror device in its focus point on sunny day?       The R5800 solar concentrator, replaced by the new R23k, is made from   an ordinary fiberglass satellite dish. It is covered in about 5800   3/8" (~1cm) mirror tiles. When properly aligned, it can generate a   spot the size of a dime with an intensity of 5000 times normal   daylight. This intensity of light is more than enough to melt steel,   vaporize aluminum, boil concrete, turn dirt into lava, and obliterate   any organic material in an instant. It stands at 5'9" and is 42"   across.   Technical details &amp; calculations:     Calculations: Area of dish aperture (elliptical)= (pi x 102cm x   73cm)/4 = 5848 sq cm       Area of focal point (circular)= pi(0.6cm)^2 = 1.14 sq cm      Dish Type= 0.7m x 1m offset focus elliptical.      Concentration Power= 5000x      Output Power Estimate = 560 watts Are these adjectives interchangeable?  I always hear: 'An Arab man.' but never 'An Arabic man.' and I always hear 'Arabic coffee' but never hear 'Arab coffee.' Transit Visa in Hong Kong for 15 hour layover between India and USA? We are (2) Indian nation and travelling from India to USA via Hong Kong airport and about 15 hours layover in Hong Kong airport. Do we need a transit visa even if only changing planes? And can we apply in Hong Kong Airport? What is the difference between fastboot oem unlock and fastboot oem unlock-go? I'm having issues unlocking my Nexus 7 2013 WiFi's bootloader, and it was suggested that I try fastboot oem unlock-go instead of fastboot oem unlock. Both seem to act the same on my device, however both also fail on my device so it is possible that the difference appears after the failure on my end comes. Regardless, I would like to know: What is the difference between these two commands? I'm not managing to find documentation. What to do when you discover a mistake in the archived copy of your PhD thesis? I've just defended my PhD in mathematics and started a postdoc. While working  on an improvement of one of the results of my thesis, I realized that there are several minor mistakes and a big bug in a proof that invalids a minor result in the thesis (about 3-4 pages out of 110). Unfortunately neither I nor my advisor or referees figured it out the mistake. Though the result is minor, it is announced in the introduction and the manuscript is on-line on an ArXiv-like server, so that I could publish a new version but not cancel the one on-line.   What is the best thing to do? Upload an errata? Upload a "revised" version of the thesis?  Publish a "revised version" of the thesis on my web-page?  Can this damage my future career, making me look not "reliable" as a researcher? "The following packages have been kept back:" Why and how do I solve it? What are the basics needed to learn quantum computing? This is a follow-up to : ulimit and cgroups are not user friendly, and besides, wouldn't work with applications that spawn separate processes, such as Chrome/Chromium for each new (group of) tabs.  The simple and effective solution, used by Windows 7 actually, is to warn the user that the OS is running low on memory. This simple warning pop-up has prevented me from having any low-memory-caused system freeze in Windows, while I kept running into them on Ubuntu distros that I was testing live (where the RAM-mounted disk would eat up 2GB alone).  So, is there some way to automatically warn the user that the available RAM is nearing zero, without the user having to keep an eye on some memory monitoring gadget? Surely  could be configured to do that? I want to prove this:  Prove that if $a \in \mathbb{Z}$ is divisible by $4$, then there exist $b$ and $c$ where $b,c \in \mathbb{Z}$ such that $a = b^2 - c^2$  I want to prove this directily:  $4\mid a $,  $a\in \mathbb{Z} \implies \exists b,c \in \mathbb{Z}, \quad$ s.t. $a=b^2-c^2$  Let $k\in \mathbb{Z}$. Then $4=a\cdot k$ and $k$ can divide $4$. Hence,  $\frac{4}{k} =b^2 - c^2 = (b-c)(b+c) \implies \dfrac{4}{k\cdot(b-c)} = b+c$  Is this proof correct? $p_1p_2...p_n +1$ is not square for $p_k = k$'th prime What are the basics of commands in Minecraft Java Edition? What are the basics of Minecraft commands? If I were to start from scratch, with no knowledge on the topic, what are some things that I need to know? Did not get notification about new privilege Does commutativity imply associativity? I'm asking this because I was trying to think of structures that are commutative but non-associative but couldn't come up with any. Are there any such examples?  NOTE: I wasn't sure how to tag this so feel free to retag it. How can I unload Oracle database tables into a csv files? I need to retrieve certain data from an Oracle 11g release 1 database and provide it as one or more CSV files. The data resides in multiple tables and/or views. All this should work via the command line. What would be the best approach to this? Is it worth buying a 5D Mark I or an EOS 1Ds II today? Finitely generated monoids- axiomatization- compactness theorem.