Electricity and Magnetism Lab 5-6 Resistors and Voltage Drops

Transcription

1 Electrcty and Magnetsm Lab 5-6 Resstors and Voltage Drops Lana Sherdan De Anza College Oct 22, 2015

2 Overvew remnder about Ohm s Law potental drops n crcuts remnder about ammeters and voltmeters usng a breadboard

3 Ohm s Law Ohm s law s the prncple used to measure resstance n the frst and second labs. We found last tme that Ohm s law held for the resstors we are usng at room temperature. We can now assume t holds for each component resstor. Remember, Ohms Law: where R s constant. V = IR In ths lab, we can use Ohm s law to fgure out the potental drop across or current through resstors that are just one part of a larger crcut.

4 Note that ths equaton reduces to Eq f the battery s deal that s, f r 0. Fgure 27-4b shows graphcally the changes n electrc potental around the Current crcut. (To and better lnk Potental Fg. 27-4b wth the Dfference closed crcut n Fg. n27-4a, amagne Crcut curlng the graph nto a cylnder wth pont a at the left overlappng pont a at b + r a Real battery (a) R Potental (V) a b a r Emf devce Fg (a) A sngle-loop crcut contanng a real battery havng nternal resstance r and emf.(b) The same crcut, now spread out n a lne.the potentals encountered n traversng the crcut clockwse from a are also shown.the potental V a s arbtrarly assgned a value of zero, and other potentals n the crcut are graphed relatve to V a. Here, resstances are n seres. V a r (b) V b R R Resstor What do we know about the current through each resstor? Va

5 Note that ths equaton reduces to Eq f the battery s deal that s, f r 0. Fgure 27-4b shows graphcally the changes n electrc potental around the Current crcut. (To and better lnk Potental Fg. 27-4b wth the Dfference closed crcut n Fg. n27-4a, amagne Crcut curlng the graph nto a cylnder wth pont a at the left overlappng pont a at b + r a Real battery (a) R Potental (V) a b a r Emf devce Fg (a) A sngle-loop crcut contanng a real battery havng nternal resstance r and emf.(b) The same crcut, now spread out n a lne.the potentals encountered n traversng the crcut clockwse from a are also shown.the potental V a s arbtrarly assgned a value of zero, and other potentals n the crcut are graphed relatve to V a. Here, resstances are n seres. V a r (b) V b R R Resstor What do we know about the current through each resstor? It must be the same for both! The resstor of value r has a voltage drop of V r = r. The R resstor has a voltage drop of V R = R. Va

6 Note that ths equaton reduces to Eq f the battery s deal that s, f r 0. Fgure 27-4b shows graphcally the changes n electrc potental around the Current crcut. (To and better lnk Potental Fg. 27-4b wth the Dfference closed crcut n Fg. n27-4a, amagne Crcut curlng the graph nto a cylnder wth pont a at the left overlappng pont a at b + r a Real battery (a) R Potental (V) a b a r Emf devce Fg (a) A sngle-loop crcut contanng a real battery havng nternal resstance r and emf.(b) The same crcut, now spread out n a lne.the potentals encountered n traversng the crcut clockwse from a are also shown.the potental V a s arbtrarly assgned a value of zero, and other potentals n the crcut are graphed relatve to V a. Here, resstances are n seres. V a r (b) V b R R Resstor What do we know about the current through each resstor? It must be the same for both! The resstor of value r has a voltage drop of V r = r. The R resstor has a voltage drop of V R = R. How could we fnd? What s the effectve resstance of r and R together? Va

7 Seres and Parallel Example Resstors 710 nchapter seres: 27 CIRCUITS + b R 1 R 2 Parallel resstors and ther Resstors equvalent n parallel: have the same potental dfference ( par-v ). the rght.) Note how traversng the c mountan a back to your startng pont In ths book, when a battery s not d s + ndcated, you can generally assume world R batteres 1 1 R are always 2 R 3 real 2 and 3 have a (a) R 3 Seres resstors and ther equvalent have the same current ( ser- ). Resstances n Seres b Fgure 27-5a shows three resstances co (a) emf. Ths descrpton has lttle to Rather, n seres means that the res that a potental a dfference V s appled 27-5a, the resstances are connected o potental dfference s mantaned acr

8 Seres and Parallel So for resstors n seres, we can use that the current s the same across both resstors to fnd: 1 the potental drop across each resstor 2 the effectve resstance of the two resstors together V R1 R 2

9 Resstors n Seres The current though resstors n seres n a loop s the same. Let the total potental dfference across two resstors be V, then V = IR 1 + IR 2 = I(R 1 + R 2 ) Then the effectve equvalent resstance of both together s just the sum R eq = R 1 + R 2 For n resstors n seres: R eq = R 1 + R R n = n =1 R

10 Seres and Parallel What about two resstors n parallel? What s the same across both resstors? V R1 R 2

11 Seres and Parallel What about two resstors n parallel? What s the same across both resstors? V R1 R 2 The potental dfference!

12 Resstors n Parallel The potental dfference across two resstors n parallel s the same. (Loop rule.) Let I be the total current that flows through both resstors: I = I 1 + I 2. (Juncton rule.) Dvdng the equaton by V : For n of resstors n parallel: I = V R eq = V R 1 + V R 2 1 R eq = 1 R R 2 1 R eq = 1 R R R n = n 1 R =1

13 Resstors vs. Capactors Table of equvalent capactances and resstances for seres and parallel. resstors capactors seres R eq = R 1 C eq = 1 C parallel 1 R eq = 1 R C eq = C

14 Example Consder the crcut pctured wth E = 12 V, and the followng resstor values: R 1 = 20 Ω, R 2 = 20 Ω, R 3 = 30 Ω, and R 4 = 8.0 Ω. b 1 3 b R 1 R 3 R 1 R 3 + R 2 + R 2 2 R 4 R 4 a c a c 1 (a) What s the current through the battery? (b) Applyng the loop rule yelds the current.

15 Example Consder the crcut pctured wth E = 12 V, and the followng resstor values: R 1 = 20 Ω, R 2 = 20 Ω, R 3 = 30 Ω, and R 4 = 8.0 Ω. b 1 3 b R 1 R 3 R 1 R 3 + R 2 + R 2 2 R 4 R 4 a c a c 1 (a) What s the current through the battery? answer: I = 0.30 A (b) Applyng the loop rule yelds the current.

16 Example Consder the crcut pctured wth E = 12 V, and the followng resstor values: R 1 = 20 Ω, R 2 = 20 Ω, R 3 = 30 Ω, and R 4 = 8.0 Ω. b 1 3 b R 1 R 3 R 1 R 3 + R 2 + R 2 2 R 4 R 4 a c a c 1 (a) What s the current through the battery? answer: I = 0.30 A (b) What s the current through resstor R 2? Applyng the loop rule yelds the current.

17 Example Consder the crcut pctured wth E = 12 V, and the followng resstor values: R 1 = 20 Ω, R 2 = 20 Ω, R 3 = 30 Ω, and R 4 = 8.0 Ω. b 1 3 b R 1 R 3 R 1 R 3 + R 2 + R 2 2 R 4 R 4 a c a c 1 (a) What s the current through the battery? answer: I = 0.30 A (b) What s the current through resstor R 2? answer: I 2 = 0.18 A Applyng the loop rule yelds the current.

18 Lab Report Ths s a 2-week lab. You wll need to prepare a lab report. Style of the lab report: pretend you are a scentst. Your goals: clearly communcate precsely what you dd, and the results you got let others know exactly how to repeat your experment, confrm your results gve an ntroducton to the reader of any theory nvolved

19 Lab report What to assume about the reader: they do not know what was on the nstructon sheet they do not know what precse equpment you used they already know how to use all of the equpment they are skeptcal

20 Lab report The lab report should contan: an ntroducton: what are you nvestgatng n ths experment the hypothess: the theoretcal predctons you are tryng to test a descrpton of the expermental procedure and all equpment used your data / measurements analyss: how well dd your data agree wth the predctons? Were there any sources of expermental error? Were they systematc or random? What would you do dfferently n the future to mprove ths experment? concluson: Does the theory seem correct? Does your data support t? If not, why not? If there are a few data ponts that devate from predctons, try to explan what may have occurred. What other related questons could you nvestgate n smlar experments?

21 Lab report Other thngs: dagrams and tables are often very helpful do not make statements wthout evdence do error analyss or gve percentage dfferences where approprate do not copy word-for-word from the nstructon sheet!

22 Procedure We wll construct these crcuts: V R1 V R1 R 2 R 2

23 Procedure On your table that wll look lke:

24 Procedure and:

25 Procedure You wll use the Smpson VOM as a voltmeter n ths experment and the HP-DMM as an ammeter to measure the current through each resstor and the potental dfference across each.

26 Meters Ammeter A devce for measurng current n a crcut. The ammeter must be connected n seres n the part of the crcut where you want to test the current. Voltmeter A devce for measurng potental dfference across a component of a crcut. The voltmeter must be connected n parallel across the component where you wsh to measure the potental drop.

27 Breadboards You wll be usng a breadboard. The nternal wrng of the breadboard looks lke ths: The top and bottom two rows are connected across the board. Columns are connected downward up untl the gap. There are no connectons across the central gap. That s a good place to put components. 1 Image from mathys/ecen2250/mydaq01/

28 Example Breadboard Crcut

29 Readng the Value of Resstors Color gude: 1 Images from orcadxcc.org.

30 HP DMM wrng To measure resstance: To measure current (ammeter):