Experiment 18Ohmic and Non-ohmic Resistances

Advanced Reading:(Serway) Chapter 27Sections 27-1 to 27-3

E q u i p m e n t :1 universal circuit board1 1-15 volt power supply1 Kelvin DMM with leads1 150 Ω resistor1 330 Ω resistor1 560 Ω resistor1 unknown resistor1 14 volt light bulb and socket1 jumper2 wire leads1 Triple-scale milliammeter

O b j e c t i v e :

The object of this lab is to determinethe resistance of several resistors byapplying Ohm's Law. Students will alsobe introduced to the resistor color code.

T h e o r y :

Ohm's law states that the current I thatf lows in a c i rcu i t i s d i rec t lyproportional to the voltage V across t h eresistance R of the circuit, or inmathematical form:

I = VR

Eq. 18-1

A device is said to be " Ohmic" if thecurrent I that f lows through thecircuit is directly proportional to thep o t e n t i a l d i f f e r e n c e a c r o s s t h eresistance. In other words, if V isdoubled then I is doubled. If an "o h m i c "device obeys the preceding criteria ,then it follows that a "non-ohmic"device does not.

In this lab, the current flow through aresistor will be measured when thevoltage across the resistors is variedand from this data, the resistance

determined. The current is measuredusing a triple-scale milliammeter.

Ammeters are connected so that thecurrent is through them. (see fig. 18-1)The ideal ammeter would have aresistance of zero so that it had noeffect on the current. In realityammeters have some resistance. On theother hand, the ideal voltmeter (theDMM in this case) has an infiniter e s i s t a n c e . ( a p p r o x i m a t e l y 1 0 7 Ω i nrea l i ty ) This keeps the voltmeter frombecoming an alternate path of currentflow around the circuit element beingmeasu red .

The potent ia l d i f ference wi l l bemeasured with the Digital multimeter,as in the Electric Field experiment.Voltmeters are connected in parallel toresistive elements in the circuit so thatit measures the potential difference oneach side of the element. The idealvoltmeter has an infinite resistance sothat only a minuscule amount ofcurrent is through the voltmeter.

Resistor Color Code

There is a color coding scheme used toidentify the value of the resistance of aresistor. The first two color bands give

R

A

0-1

5v

Pow

er

Sup

ply

+-

figure 18-1

the first two digits in the resistancevalue. The third band gives themultiplier for the first two in powersof ten. The last color is the tolerance.For example, a resistor that has two redbands and a black multiplier band, hasa resistance of 22Ω. The figures belowgive the color code.

First Digit

Second Digit

Multiplier

Tolerance

figure 18-2

P r o c e d u r e :

1. Make a simple series circuit withthe 150 Ω (as shown in fig. 18-1), usingthe power supp ly , mi l l i ammete r ,shunts, and wire leads. Have thec i r c u i t a p p r o v e d b y y o u r

i n s t r u c t o r b e f o r e t u r n i n ganything on .

CAUTION: NEVER HOOK ANAMMETER IN PARALLEL WITH APOWER SUPPLY. IT HAS ARESISTANCE CLOSE TO ZERO ANDCOULD BE DAMAGED.

2. Plug in the power supply and adjustthe voltage until the DMM reads a o n evolt potential difference across theresistor. Measure the current at thisvoltage. (Have the input wires to themilliammeter in such a position so thatthe meter reads as close to full scale aspossible . )

3. Increase the voltage in one voltincrements up to 12 volts, measuringthe current through the resistor ateach voltage level. Record all values ofcurrent I in amperes and voltage V involts .

4. Repeat this procedure for the330 Ω , 560 Ω, and unknown resistors

5. Graph I vs. V and plot a best fit linefor each of the resistors on the samegraph. Calculate the slope of each line.From these slopes, obtain the value ofthe resistances R for the resistors. Besure to label each of the slopesa p p r o p r i a t e l y .

6. Measure the resistance of eachresistor using the ohmmeter functionof the DMM. Do this by placing theinput wires in the correct holes on theDMM and turning the dial to the ohms( Ω ) postion. The DMM provides apotential difference between the leadsand measures the amount of currentthrough the resistance.

7. Replace the resistors with the lightbulb and repeat steps 2 and 3 for thelight bulb. Plot a graph of I vs. V forthe light bulb, only this time connecteach data point with a best fit curve.

Color Number Multiplier

Black 0 100

B r o w n 1 101

Red 2 102

O r a n g e 3 103

Yellow 4 104

G r e e n 5 105

Blue 6 106

Violet 7 107

G r a y 8 108

W h i t e 9 109

To le rance Gold 5%S i l v e r 10%no band 20%

figure 18-3

Q u e s t i o n s / C o n c l u s i o n s :

1. Calculate the percent differencebetween the color code value and theexperimental value found in thisexperiment for each resistor. Do thesevalues fall within the bounds of theprecision printed on the sides of theresistors? If they do not, what mightbe the reason for this?

2. What is the value of the unknownresistor determined from the graph?Ca lcu la t e the pe rcen t d i f f e rencebetween the value obtained from thegraph and the ohmmeter value.

3. The resis tors used in thisexperiment are 2 watt resistors. Whatis the maximum power output of the150Ω resistor when 12 V is appliedacross it?

4. The power output of a circuit isgiven by

P = i2R = V 2

R= iV Eq. 18-2

Calculate the power output of eachresistive element when a potential of12 volts is applied.

5. Verify dimensionally that equation18-2 is correct. What are the units ofpower output?

6. Is the graph of I vs. V for the lightbulb linear? What does this tell youabout the resistance of a lightbulb asthe filament gets hotter?