Error In Capacitance
a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Physics Questions Tags Users Badges Unanswered Ask Question _ Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Calculating Systematic Error for capacitor charge time constat up vote 1 down vote favorite 1 I need to calculate systematic error for $\tau$ in capacitor's charging formula( $V_c(t)=V_s(1-e^{-t\over\tau})$ ) I converted it to : $\tau=-{t \over ln(1-{V_c \over V_s})}$ and continued by doing: $ln(\tau)=ln(-t)-ln(ln(1-{V_c \over V_s}))$ then tried to derivative: ${d\tau \over \tau}={dt \over t}- ...$ I can't go ahead any more! What about discharge equaltion ( $V_c(t)=V_0 e^{-t\over\tau}$ )? How should i continue and get result for $d\tau \over \tau$? capacitance share|cite|improve this question edited Nov 25 '11 at 13:56 asked Nov 25 '11 at 11:18 RYN 1085 add a comment| 1 Answer 1 active oldest votes up vote 2 down vote accepted You should work out this $$d\tau=-\frac{dt}{\ln\left(1-\frac{V_c}{V_s}\right)}$$ $$+\frac{t}{\ln^2\left(1-\frac{V_c}{V_s}\right)}\left(-\frac{dV_c}{V_s}+V_c\frac{dV_s}{V_s^2}\right)$$ The next step is to divide by $\tau$ and you will get $$\frac{d\tau}{\tau}=\frac{dt}{t}+\frac{\tau}{t}\frac{dV_c}{V_c}-\frac{\tau}{t}\frac{V_c}{V_s}\frac{dV_s}{V_s}$$ share|cite|improve this answer answered Nov 25 '11 at 13:13 Jon 1,941715 Hi, Thanks , But how you got $+\frac{t}{\ln^2\left(1-\frac{V_c}{V_s}\right)}\left(-\frac{dV_c}{V_s}+V_c\frac{dV_s}{V_s^2}\right)$ from $d\tau=-\frac{dt}{\ln\left(1-\frac{V_c}{V_s}\right)}$ ? and can you give a help about discharge equation that I added? –RYN No
Help Suggestions Send Feedback Answers Home All Categories Arts & Humanities Beauty & Style Business & Finance Cars & Transportation Computers & Internet Consumer Electronics Dining Out Education & Reference Entertainment & Music Environment Family & Relationships Food & Drink Games & Recreation Health Home & Garden Local Businesses News & Events Pets Politics & Government Pregnancy & Parenting Science & Mathematics Social Science Society & Culture Sports Travel Yahoo Products International Argentina Australia Brazil Canada France Germany India Indonesia Italy Malaysia Mexico New Zealand Philippines Quebec http://physics.stackexchange.com/questions/17417/calculating-systematic-error-for-capacitor-charge-time-constat Singapore Taiwan Hong Kong Spain Thailand UK & Ireland Vietnam Espanol About About Answers Community Guidelines Leaderboard Knowledge Partners Points & Levels Blog Safety Tips Science & Mathematics Physics Next Errors capacitor experiment? Hi , I am wondering what type of errors I should calculate for the charge/ discharge of a https://answers.yahoo.com/question/index?qid=20111105071741AAgRxxm capacitor experiment? Update: Thanks Laura , some good info , but I am wondering what type of calculations should I do for errors , eg standard deviation etc Follow 1 answer 1 Report Abuse Are you sure you want to delete this answer? Yes No Sorry, something has gone wrong. Trending Now Women tied Emilia Clarke Michelle Wie Emily Blunt Kellyanne Conway Contact Lenses Oregon Ducks Office 365 Online Nursing Course Joey Bosa Answers Best Answer: I'm not an expert but I have written electrical textbooks. There are going to be certain losses (the capacitor stores a charge and there will be some wasted power in the form of HEAT). Also, when you discharge the capacitor, the tool used to discharge it will waste some of the power. The environment in which the capacitor is placed will also contribute to errors. Nearby devices can have an impact upon the capac
initial voltage to the rate of decay of the voltage across the capacitor during the discharge. 1. Introduction The aim of this experiment is to study the discharge of capacitors through filament lamps as a function of the http://academia.hixie.ch/bath/capacitor/home.html initial voltage across the capacitor, and, if possible, model this process. The initial brief (Bath, 1998) explained that the voltage across a charged capacitor of capacitance C, when discharged through a resistor of resistance R, varies exponentially according to the following equation. (1) -t RC Q = Q0 e Constants In all equations quoted in this report, V is the voltage across the capacitor, t is the time elapsed since the start of the error in discharge, V0 is the value of V at t=0, and C is the capacitance of the capacitor being discharged. This is covered in most introductory text books, for example Bell, 1978. If R is not a constant but a function of the voltage to which the capacitor is initially charged (i.e., R = f(V0)), then the relationship is no longer simply exponential. This can occur, for instance, if the resistor is in the form of error in capacitance a filament lamp that rapidly increases temperature when a current flows through it. Some further points of theory are covered in the appendix. In this case, one would expect that the graph would start non-exponentially, since at voltages roughly > 1V the lamp is lit, and thus non-ohmic, and then when the voltage reaches (and goes below) 1V, the curve would become exponential as for an ohmic resistor. 2. Method 2.1 Circuit At the centre of circuit lay the capacitor being tested. The other components in the circuit were the voltage source, a digital multimeter (DMM), a chart recorder, the filament lamp, and a two-way switch. The DMM was wired across the voltage source and was used to set the initial voltage across the capacitor. The chart recorder was similarly wired across the capacitor. The switch was used to select whether the capacitor should charge or discharge by being connected to the capacitor on the common terminal, the voltage source on one of the two other terminals, and the lamp on the final terminal. 2.2 Readings Readings were taken for each capacitor/initial voltage pair several times. This was done by recording the voltage drop across the capacitor with the chart recorder. (The graphical output was then measured by hand before being analysed electronically). Furthermore, to reduce the error in the
be down. Please try the request again. Your cache administrator is webmaster. Generated Tue, 11 Oct 2016 17:43:38 GMT by s_ac15 (squid/3.5.20)