# Relationships Between Frequency, Capacitance, Inductance and Reactance.

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1 P Physics Relatinships between f,, and. Relatinships Between Frequency, apacitance, nductance and Reactance. Purpse: T experimentally verify the relatinships between f, and. The data cllected will lead t the cnclusin the is inversely prprtinal t and f. This activity will als verify the capacitive reactance frmula. Equipment: Patch rds, Alligatr lips 2 DMMs apacitance Bx Functin Generatr Decade Resistance Bx Tridal inductrs (5H) R meter Thery: A battery cnnected in series with a resistr frms a simple circuit where Ohm's law can be applied. Using Ohms law, the current in the circuit is given by Where ε ο is the battery vltage, and R is the resistance. ε = Eq. 1 f a capacitr is placed a series circuit with a dc vltage surce such as a battery, the current thugh the circuit will be exactly zer. f yu replace the battery with an ac (sinusidal) vltage surce, then the current will nt be zer. nstead it will be a sinusidal functin with amplitude given by: ε R 1, where = 2πf = Eq. 2 n sme ways, then the capacitr is a type f "A resistr" with effective resistance given by. Prf: The vltage drp acrss a capacitr is given by q V =. Since q = idt and i is a sinusidal f the frm: i( t) = sin 2πft then ( ) 1 f 8

2 P Physics Relatinships between f,, and. q( t) = sin( 2 π ft) dt = cs( πft) 2πf 2 thus Vc can be written as: V = cs( 2πft) = V cs( 2πft). max 2πf We define the reactance f the capacitr as: Thus, this implies that we can calculate c by Eq. 3. Vmax = Eq. 3 max 1 = = Eq. 4 2πf 2πf f an inductr is placed in a series circuit with a sinusidal vltage supply, then the current is given by: ε = where = 2πf n the same way, an inductr can be cnsidered an A resistr, with effective resistance. Prf: The vltage drp acrss an inductr is given by di V =. dt f i( t) = sin( 2πft), then V = 2πf cs 2πft and we can define the inductive resistance by: thus, max ( ) V max = Eq. 5 2πf = = 2πf. Eq. 6 This implies that we can calculate c using Eq. 5 by measuring the vltage drp acrss the inductr and the current thrugh the circuit. We can als calculate frm Eq. 6 with knwledge f f and. 2 f 8

3 P Physics Relatinships between f,, and. Experiment and Analysis: Part A 1. a. nstruct the circuit shwn in Figure 1 belw using a 1-µF capacitr fr 1. Use the R meter t determine a "gd" value fr the capacitance. Next, set the generatr frequency t apprximately 100 Hz. Adjust the utput cntrl fr apprximately 1-3 V acrss the capacitr. Recrd the current flwing thrugh the capacitr. Nte: yu may have difficulty using the DMM meter t recrd the current! t is likely t be rather small. An alternative strategy is t set up the circuit as shwn in Figure 2. The resistance shuld be n the rder f 1 / 2πf. Yu can then measure the vltage acrss the resistance bx and divide by the resistance ( = V/R) t determine the current. Keep in mind that yu must use figure (1) t measure the vltage acrss the capacitance, and figure (1b) t measure the vltage acrss the resistr. Als remember nt t change the resistance when yu measure vltage acrss the capacitr. Nte that the DMM measures RMS values fr current: rms = (Essentially, this means that that = the DMM reading multiplied by 2 ). V DMM A Vltage readings are als rms values, s that V =. rms 2 2 R Resistance Bx Functin generatr + _ ~ Vc DMM set n A vlts. Figure 1 Measuring the Vltage with the DMM 3 f 8

4 P Physics Relatinships between f,, and. Functin generatr + _ ~ R Resistance Bx Vr DMM set n A vlts. Figure 2 Measuring the current using the resistance bx. b. Using yur measured current and vltage, cmpute the reactance f the capacitr using = V /. Yu can use the DMM readings fr V and since the factr 2 cancels ut. c. alculate the reactance using the reactance frmula 1 = 2πf d. Are the values cmputed in Steps 1b and 1c within 10 percent f each ther? f nt, use the R meter t get gd values fr the capacitance, and resistance. f they check ut, then use the scillscpe t determine the perid and frequency f the functin generatr. Als be sure that yu have a "gd" sine wave. When yu are satisfied, enter yur results in Table 1. e. D yur results cnfirm the reactance frmula (within the tlerances f the meter, the generatr and the capacitr )? That is, des = V? 2. a. Suppse the generatr frequency is changed t 50 Hz while the vltage remains at 3 V. What will happen t the reactance? b. What will happen t the circuit current? c. hange the generatr frequency t 50 Hz and recrd the new current in Table 1. d. Des yur answer t Step 2c supprt yur answer t Step 2b? e. Hw much current wuld yu expect if the frequency were changed t 200 Hz and V remained at 3 V? f. hange the frequency t 200 Hz and adjust the generatr fr 3 V acrss the capacitr. Recrd the current. 4 f 8

5 P Physics Relatinships between f,, and. 3. hange the capacitr in Fig. 1 t 0.15 µf. Repeat Steps 1 and 2. Enter yur results in Table. 4. D yur values fr V and agree in each case? f nt, is the agreement better at high r lw frequencies? Why d yu think this is? Part B 1. Repeat the prcedure frm Part 1 using the 5H inductr in place f the capacitr. Use the R meter t get a "gd" value fr inductance. mplete Table 2 using Eqs. 5 and 6. Yur values fr shuld agree within 10 r 15% (due t uncertainties in measuring A current accurately). f yu are using the resistance bx t determine current, yu will have t change the setting s that enugh vltage is drpped acrss it t be measured. n general, set R bx apprximately equal t 2πf fr whatever frequency yu are using. A DMM n A current setting Functin generatr + ~ - Vc DMM set n A vlts. Figure 3 2. heck t see if the reactance determined abve agrees with the value calculated by the reactance frmula. alculate and recrd the reactance using the frmula = 2πf. The reactance calculated here shuld be within 15% f the reactance yu listed in Table 2. f it is nt, recheck yur measurements and yur calculatins. 3. hange the frequency f the generatr t 500 Hz. Measure the utput vltage f the generatr. Nte that the utput vltage is likely t drp. Make the measurements and calculatin necessary t cmplete the secnd rw f the table. Des yur data table supprt yur predictins abut what happens t the reactance and the current? 5 f 8

6 P Physics Relatinships between f,, and. 4. hange the generatr frequency t 1000 Hz. Frm the reactance yu determined in the first tw rws f Table 2, predict and recrd the reactance yu will have at 1000 Hz. mplete the third rw f the table t check yur predictin. Results: Write at least ne paragraph describing the fllwing: what yu expected t learn abut the lab (i.e. what was the reasn fr cnducting the experiment?) yur results, and what yu learned frm them Think f at least ne ther experiment might yu perfrm t verify these results Think f at least ne new questin r prblem that culd be answered with the physics yu have learned in this labratry, r be extraplated frm the ideas in this labratry. 6 f 8

7 P Physics Relatinships between f,, and. lean-up: Befre yu can leave the classrm, yu must clean up yur equipment, and have yur instructr sign belw. Hw yu divide clean-up duties between lab members is up t yu. lean-up invlves: mpletely dismantling the experimental setup Remving tape frm anything yu put tape n Drying-ff any wet equipment Putting away equipment in prper bxes (if applicable) Returning equipment t prper cabinets, r t the cart at the frnt f the rm Thrwing away pieces f string, paper, and ther detritus (i.e. yur water bttles) Shutting dwn the cmputer Anything else that needs t be dne t return the rm t its pristine, pre lab frm. certify that the equipment used by has been cleaned up. (student s name),. (instructr s name) (date) 7 f 8

8 P Physics Relatinships between f,, and. TABE 1 V f c (thery) c (exp) %diff Frequency f urrent Vltage acrss 1, V 1 (measured) TABE 2 nductive Reactance = 2πf nductive reactance % V = difference 100 Hz 500 Hz 1000 Hz 8 f 8

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### I understand the new topics for this unit if I can do the practice questions in the textbook/handouts 1 U n i t 6 11U Date: Name: Sinusidals Unit 6 Tentative TEST date Big idea/learning Gals In this unit yu will learn hw trignmetry can be used t mdel wavelike relatinships. These wavelike functins are called

### Q1. A) 48 m/s B) 17 m/s C) 22 m/s D) 66 m/s E) 53 m/s. Ans: = 84.0 Q2. Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 1 Q1. A string, f length 0.75 m and fixed at bth ends, is vibrating in its fundamental mde. The maximum transverse speed

### MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b . REVIEW OF SOME BASIC ALGEBRA MODULE () Slving Equatins Yu shuld be able t slve fr x: a + b = c a d + e x + c and get x = e(ba +) b(c a) d(ba +) c Cmmn mistakes and strategies:. a b + c a b + a c, but

### Trigonometric Ratios Unit 5 Tentative TEST date 1 U n i t 5 11U Date: Name: Trignmetric Ratis Unit 5 Tentative TEST date Big idea/learning Gals In this unit yu will extend yur knwledge f SOH CAH TOA t wrk with btuse and reflex angles. This extensin

### Corrections for the textbook answers: Sec 6.1 #8h)covert angle to a positive by adding period #9b) # rad/sec U n i t 6 AdvF Date: Name: Trignmetric Functins Unit 6 Tentative TEST date Big idea/learning Gals In this unit yu will study trignmetric functins frm grade, hwever everything will be dne in radian measure.

### Section 5.8 Notes Page Exponential Growth and Decay Models; Newton s Law Sectin 5.8 Ntes Page 1 5.8 Expnential Grwth and Decay Mdels; Newtn s Law There are many applicatins t expnential functins that we will fcus n in this sectin. First let s lk at the expnential mdel. Expnential

### Review Problems 3. Four FIR Filter Types Review Prblems 3 Fur FIR Filter Types Fur types f FIR linear phase digital filters have cefficients h(n fr 0 n M. They are defined as fllws: Type I: h(n = h(m-n and M even. Type II: h(n = h(m-n and M dd.

### Q1. In figure 1, Q = 60 µc, q = 20 µc, a = 3.0 m, and b = 4.0 m. Calculate the total electric force on q due to the other 2 charges. Phys10 Secnd Majr-08 Zer Versin Crdinatr: Dr. I. M. Nasser Saturday, May 3, 009 Page: 1 Q1. In figure 1, Q = 60 µc, q = 0 µc, a = 3.0 m, and b = 4.0 m. Calculate the ttal electric frce n q due t the ther

### 11. DUAL NATURE OF RADIATION AND MATTER 11. DUAL NATURE OF RADIATION AND MATTER Very shrt answer and shrt answer questins 1. Define wrk functin f a metal? The minimum energy required fr an electrn t escape frm the metal surface is called the

### Pipetting 101 Developed by BSU CityLab Discver the Micrbes Within: The Wlbachia Prject Pipetting 101 Develped by BSU CityLab Clr Cmparisns Pipetting Exercise #1 STUDENT OBJECTIVES Students will be able t: Chse the crrect size micrpipette fr

### Thermodynamics Partial Outline of Topics Thermdynamics Partial Outline f Tpics I. The secnd law f thermdynamics addresses the issue f spntaneity and invlves a functin called entrpy (S): If a prcess is spntaneus, then Suniverse > 0 (2 nd Law!)

### MODULE FOUR. This module addresses functions. SC Academic Elementary Algebra Standards: MODULE FOUR This mdule addresses functins SC Academic Standards: EA-3.1 Classify a relatinship as being either a functin r nt a functin when given data as a table, set f rdered pairs, r graph. EA-3.2 Use

### Potential and Capacitance Ptential and apacitance Electric Ptential Electric ptential (V) = Electric ptential energy (U e ) per unit charge () Define: ptential energy U e = 0 at infinity (r = ) lim U 0 r e Nte the similarity f

### CHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came. MATH 1342 Ch. 24 April 25 and 27, 2013 Page 1 f 5 CHAPTER 24: INFERENCE IN REGRESSION Chapters 4 and 5: Relatinships between tw quantitative variables. Be able t Make a graph (scatterplt) Summarize the

### Pages with the symbol indicate that a student should be prepared to complete items like these with or without a calculator. tan 2. Semester Eam Review The semester A eaminatin fr Hnrs Precalculus cnsists f tw parts. Part 1 is selected respnse n which a calculatr will NOT be allwed. Part is shrt answer n which a calculatr will be allwed.

### In a radioactive source containing a very large number of radioactive nuclei, it is not Simulated Radioactive Decay Using Dice Nuclei Purpose: In a radioactive source containing a very large number of radioactive nuclei, it is not possible to predict when any one of the nuclei will decay.

### Math Foundations 20 Work Plan Math Fundatins 20 Wrk Plan Units / Tpics 20.8 Demnstrate understanding f systems f linear inequalities in tw variables. Time Frame December 1-3 weeks 6-10 Majr Learning Indicatrs Identify situatins relevant

### M thematics. National 5 Practice Paper E. Paper 1. Duration 1 hour. Total marks 40 N5 M thematics Natinal 5 Practice Paper E Paper 1 Duratin 1 hur Ttal marks 40 Yu may NOT use a calculatr Attempt all the questins. Use blue r black ink. Full credit will nly be given t slutins which cntain

### Capacitance. Applications of Electric Potential. Capacitors in Kodak Cameras 3/17/2014. AP Physics B 3/7/04 apacitance P Physics B pplicatins f Electric Ptential Is there any way we can use a set f plates with an electric fiel? YES! We can make what is calle a Parallel Plate apacitr an Stre harges between

### This section is primarily focused on tools to aid us in finding roots/zeros/ -intercepts of polynomials. Essentially, our focus turns to solving. Sectin 3.2: Many f yu WILL need t watch the crrespnding vides fr this sectin n MyOpenMath! This sectin is primarily fcused n tls t aid us in finding rts/zers/ -intercepts f plynmials. Essentially, ur fcus

### ECEN 4872/5827 Lecture Notes ECEN 4872/5827 Lecture Ntes Lecture #5 Objectives fr lecture #5: 1. Analysis f precisin current reference 2. Appraches fr evaluating tlerances 3. Temperature Cefficients evaluatin technique 4. Fundamentals

### ( ) kt. Solution. From kinetic theory (visualized in Figure 1Q9-1), 1 2 rms = 2. = 1368 m/s .9 Kinetic Mlecular Thery Calculate the effective (rms) speeds f the He and Ne atms in the He-Ne gas laser tube at rm temperature (300 K). Slutin T find the rt mean square velcity (v rms ) f He atms at + - Hmewrk 0 Slutin ) In the circuit belw: a. Find the magnitude and phase respnse. b. What kind f filter is it? c. At what frequency is the respnse 0.707 if the generatr has a ltage f? d. What is the Physics 1 Lecture 1 Tday's Cncept: Magnetic Frce n mving charges F qv Physics 1 Lecture 1, Slide 1 Music Wh is the Artist? A) The Meters ) The Neville rthers C) Trmbne Shrty D) Michael Franti E) Radiatrs