It. c -t TECH to to Lab # 1 Ohm's Law . . Condll ted 212211 3 By yow'name .. ,-) r ) , I I­ 1', ,-t INTRODUCTION During the nineteenth century so many advan ces were m ade 10 understanding the electrical ~ nl2-£..,:' ) nature of matter that it has b en called the "age of electri city." One such advance was made by 1\ '?( j" rt" t;; c'r 00'.. . . an investigator named Georg Si mon O hm. O hm was interested in examining the relative conductivity of me tals a nd in investi gating the relationship betwee n the e lectromoti ve forc e (potential difference) and the current in a conductor . By taking w ires made from differe nt materials but having the same thickness, passi ng a current th ro ugh thes e wires and meas ur ing the e lectromotive forc e (i .e., th e potential difference between the ends of the conducting wire). he was able to e 'perimenta lly determ ine the r lati ve conductivity of certain metals such as silver, copper, and gold. In another experiment using a p iece of apparatus that he built himsel[ Ohm investigat d the effect of current in a conductor on the voltage drop across the conductor. He found th at G r a given conductor the voltage drop was directly propo rtional to the curre nt in the wire . When voltage is plotted ag ainst th e cll rr nt in a given conductor, the data can be fit ted to a stra ight line , r the slope of which is the l'eSistal lce of the conductor. T his result was p ublished in 1826. In recognition of Ohm 's work, thi s emp irica l relationship bears his name. DISCUSSION OF PRINCIPLES Ohm's Law can be '10 ) ritten algebraicall y as: \.; ~...) v= JR (1) V J =­ (2) R V R=­ (3) J e~ Lab #1- Ohm's Law Your Name 1 JI..... I J't;-j f">....... i ',,<pJ. / '1> -' L where V represents the p otc Ilt i a ~drop ac ross the conductor (measured in vo lts), I the CUITcnt in the conductor (measured in amperes), and R the res istance of the conductor measured in units F called "ohms" (sy mbolized by ~ n, upper-case Greek omega). Re istance and Resistors Resistance is a propert_ of materials. Res istors are cond ucti ng devices made fro m materials which satisfy Olun's Law. If the potential difference across a resistor is set at 1 volt, and if a current of 1 amp is meas ured in the conduc tor, th e n its re istance is determined to be 111, o r 1 W. Instead of usi ng th in "vires as Ohm d id in his original experiment, you will replicate his results lIsing small cylindrical ceramic r sistors . You wi ll notice colored bands on the resistors. These bands D nn a code that indi cates the resistance of the resistor. Later in thi s experiment you willlearn ho w to read lhis color code . 13 ~ Combinations of Resistors Resistors can be combined in simple circuit arrangements that increase or decrease the overal l resistance in the circuit. These arrangements are called parallel and series circui ts. Figure 1 shows the resistors in a parall el arrangement and Figure 2 illustrates two reo istors connected in seri es. Figure 1 - Parallel Circuit Figure 2 - Series Circuit In order for charges to move in a conductor, there must be a potenti al difference across the conductor. In order for charges to move through a circuit, there m ust be a complete path lead ing away from and bac k to the source of emf (V AB in F igure 1). c Lab #1- Oh m's Law b Your Name 5c. r Iff:; 2 As you can see, in the paralle l arrange ment shown in Figure 1, the current can divide at the junction A and recombine at j unction B . T herefore , the Cllnelh thro ugh R, and R, mav be - " .... diffe rent. Notice that in th is case I ~ (4 ) T hat is, the pot ntial drop across each resi stor is the same . In the series arrangement shown in Figure 2 the current in the circuit goes through each res istor. If we compute the pote ntial drop V J across R, usi ng Ohm ' s Law, it is merely; .:; ;:.--.T (5) Likewi se the drop across R2 is: (6) The potential drop across both resistors is: (7) One can think of the applied voltage V AB being divided between the two series res istors TS.l and Using some simpl e algebra and your understanding of the potential drops in a simpl e series or parallel circuit, the relationships for determining equivalent res istance for re i. tor in series and/or parallel can be derived. These relationships are: 1 1 1 1 Re quivalent Rl R2 Rn ----=-+-+­ Lab ttl - 0 hm's Law Your Name (8) 3 (The reciprocal of the eq uivalent res istance IS the sum of the re ciprocals of the indi idual resi stances. ) " • (Series ) .....­ S,,,,,-­ t::: 1tt.. 4 ,",,",' Requivalent = Rl + R2 + R n (9) .) .----­ f.\. (The equivalent resistance is simply the sum of the individual resistances.) As sugges ted by th eq uations above, the sums include a term for each resistor in the circuit. pl/\ PROCEDURE: Determinillg Resistance We wi ll use a computer and softwa re to act as our battery and voltmeter, while we wil l monitor the CUlTent with a hand-held mul timetcr. Do not turn on the power to your c ircuit until your lab instructor has ch eked your wiring. 1.) T urn on th . computer and monitor, the Interface Device, and the Power Amplifier. a. Plug the rear output of the Power Amplifier into Analog Channel C of the fnte rface . b. Plug a vo ltage probe into nalog Channel A of the Signal Inte rface. 2) Open the fol der "LABS" by double clicking on the folder if it is not already open. On ce tbe Labs folder is open . open the " Ohm' s Law" file. The file should open to 10 k like th at shown in F igure 3 below. The window shows both a digital and analo g voltmeter, both measuring the voltage fro m the voltage probe. IGI L lSI Qh., · , [!]~[!J Ot"St.t.! D .. ~ (';1 C)n fll l GlI! l'l er l'll or O[ AC W4,",El forrn II lrvl"UI""·I····+.....I"'--10 ~ DCVI)U"lje 100 V °Al1P m Au t ON/ OFf UOI\o q e l UJ 0.0 0 I~!I~ ~ W 1 0 _ Uollo • • 10 IUI _ 0 10 ~ '"'.. ·· ' 1·'·''' ~ ~ " Figure 3 - Start Up Screen Lab tt1- Ohm's Law Your Name <- r I ''1 4 3.) Connect the circuit shown in Figure 4, using the resistor labeled as " 100 W" on th circuit board . We will use a small multimcter as an ammeter. Set the multimeter to the range marked 2 DCA. + Volt3.ge probes to interface + V Voltmeter (co mp uter interface) Figure 4 - Circuit Dia gram for Proc edure A L- ) G Our "voltmeter" is actually our computer connected to the Signal Int rface. Vo ltmeters have a relatively hi gh resi stance and are placed in parallel with the resistor. Ammeters. wi th their relati vely low resistance, are placed in seri es with the resistor. 4.) Select the Signal Gen rato r window by clicking in that window. The Signal Generator wi ndow is shown in Figure 5. Turn on the signal generator by clicking on the 0 button . Cl ick the DC button if it is not already highlighted. Set the DC voltage to 1 V by cli cking on the small up arro w next to the voltage setting. \"" CIDSe Button \ (C lDse Window by clicking he re) 0 NI OFF ~..i tch-----y Sig nal Generat or ~- Volt3.ge Adjustme nt Figu re 5 - Signal Generator Window La b #1- Ohm's Law Your Name '- r: \ I' I '1 5 5.) Pre '5 Command M to start taking data. With R J in the circuit, obtain six current and oltage measurements by increasing the voltage in I-volt steps . Record t his information in the data table below. Ohm's Law Data ~ II i I ! i ! 0v Voltage (volts) III 1 I! Current (amps) II II II Ii II 2 3 4 I I ~ ~ I~ I! 5 6 I Reading the resistor code The resistance of most ceramic res isto rs can be determined from the col ored bands pri nted on the resistor. Each color re presents a digit from 0 to 9 (see Figure 6). 1-800-972-222 ~ III A J 732-381-8020 EieCiruni, b press I RS R iII1f':lI"·"·,,,. e/exp. COlli Figure 6 - Resistor Color Code t::-c Ph"'" Th first two bands give the mantissa of a number in scientific notation: the third gi ves the power often. The fourth band gi ves the tole rance (uncertainty expressed as a percentage) in tbe value of Lab #1- Ohm's Law Your l\Jame 6 ) - .... L.s. e cl". the resistance (Gold C.: ,'-G. L.~" ~ cc = ~ 5%; Silver :J ;; 10%, no 4th band ~~O%). Th fifth band, if present, gives the power rating of the resist r. We will not be concerned with the 5th band. however in order to know whic h end of a resistor to "start" from when reading the color code, it may be useful to remember that the 4th banel , if present, is metallic in color (gold or silver). ~l r Results In this section, all experimental results are presented. Theo retical predictio ns may be presented here to provide a com pari on with the experimental data. Be sure that all figures and tables are properly introduce I and labeled. B sure to provide sufficient discussion of all data presented, as well as a compaJis n of analyti cal , theoretical, and experimental res ults. Make every eff011 to account for any disparities between the theory and exp rimental results as best you can. ote that all figures and tables must be mentioned and described in the body of the t xt. Don't inc lude a figure and say nothing of it in the body of the text. Refer to each by number (e.g., Figure 1). \Iso make sure to adequate ly answer all questions posed in the lab hand ut. Use subsection. as ne cled. \ _ or ~~ (I\l -::=::­ ~ul" ~ ~I/~C-) Discus ion or Analysis sually you will be requi red to analyze your results and draw conclusions from the :s exp~ri men t. Conclusion Th is section you make a declarative statement whether the experiment succeeded and how you cmne to that determination. r u / ~~-------------------~ 1 http://homepages.u d ayton.edu/~hardierc/ECE401/ECE401L/Formal Report Guidlines.pdf Lab ttl - Ohm's Law Your Name 7 ) the resistance (Gold = ~5 %; Si lver =i s"" L, ei.· (" l r c. ,I.e­ L. f; ".1 ± 10%, no 4th band :~O%). The fi fth band, if present, gives the power rating of the resistor. We will not be concerned with tht: 5th band. however in order to know which end o f a resistor to "start" from when read ing the co lor code, it may be useful to remem ber that the 4th band, if present, is metallic in color (go ld or silver). ~v Results In this section, all experimental results are presented. Theoreti caJ predicti ons may b presented here to provide a com parison with the experimental data. Be sure that all figures and tables are properly introd uced and labeled. Be sure to provide sufficient discllss ion of all data presented. as well as a compariso n of ana lyti cal, theoretical, and experimental resu lts. Make every c1Tort to account fo r any disparities between the theory and experi mental resu lts as best yo u can . No te that all fi gures and tables must be mentioned and described in the body of the text. Don't incl ude a figure and say noth ing of it in the body of the text. Refer to each by n umber (e .g., Figur 1). Also make sure to adequat Jy a nswer all questions posed in the lab handout. l needed. ,- r=u(,,} f'loJ ( (~.~/~ ~L<J'h 5 Ire-) se subsections as L-~ Discussion or Analysis sually you will be requ ired to analyze your results and draw con lusions from the exp riment. ~ Conclusion Thjs section you make a declarative statement whether the experiment succeeded and how you came to that dd erm ination. , (v ~ ~----------------------­ _" 1 http: // homepag es. udayton. e du/~hardierc/ ECE401/ECE401L/Formal Report Guidlin es. pdf Lab #1- Ohm's Law Your Name 7 r. I t -'.., ::t