APSC 100 Module 2 Lab 3 - Electrical Resistive Behaviour of Three Devices.docx

of 13Ian Ip

10011223

Lab #3: Electrical Resistive Behaviour of Three Devices

February 20, 2012

Ian Ip10011223Section 5

Email: 0imhi@queensu

Lab partner: Blair Hanbury

APSC100 Module 2

ABSTRACT

An experiment was designed and conducted to investigate the resistivity properties of an unknown standard resistor, LEDs and light bulb. Each of these devices went under testing in an established circuit powered by a DC power supply with current and voltage monitored through two multimeters. The experiment worked within the parameter of 12V to -12V on the power supply and data sets were collected from within this range. Results indicated that the unknown standard resistor was ohmic and has a resistance of 22 Ohms. The LEDs was proven to be non ohmic and the cut in voltage of the LEDs in series were 3.7 V. Lastly, the light bulb in the circuit also displayed non ohmic properties and it was discovered that the light bulb filament’s resistance increases as temperature increases. Qualitative observations also show that the light bulb only light up after a certain current voltage has been reached. All in all, the regression analysis showed that the data recorded fitted closely with the line of best fit and other regression tools.

I verify that this formal report is my own individual work and has not been copied in whole or in part from another source (with the possible exception of equations, tables and/or diagrams from the experimental descriptions on the APSC100-2 website). Furthermore, I have not and will not lend this report (electronic or hardcopy) to any other student, either now or in the future. Signed:__________________________

of 13Ian Ip

10011223

1.0 Introduction

The resistivity of any given devices in a circuit can be measured by measuring the current I through the device and the voltage V (Differences in electrical potential prior and after of the device). Effectively, the resistance of the circuit (or part of the circuit: i.e. a particular device in the circuit) can be determined by the following equation:

R=VI

Where resistance R is measured in Ohms, voltage V is measured in Volts and current I is measured in amps. Essentially, the equation is a rearranged version of Ohm’s Law. Ohm’s law state that current is equal to the product of voltage and the inverse of resistance. By plotting current through a device as a function of voltage, one can determine the resistivity of the device. If the graph produces a straight line, then the device under test is an ohmic resistor because resistance is constant. From figure 1, ohmic resistors are typically metals under moderate current at constant temperature. On the other hand, devices with non-linear relationship describe non-ohmic resistors such as semiconductors as shown in figure 2. The resistance of most resistors increase with an increase in temperature (Semiconductors does the opposite and decrease with temperature).

In

this lab, the resistive property of three different devices will be investigated. The three devices are standard resistors, light emitting diode (LED) and a light bulb. By measuring the current and

Figure 1: The Voltage (x) and Current (y) plot of an ohmic resistor

Figure 2: An example of a Voltage (x) and Current (y) plot of non-ohmic resistor

of 13Ian Ip

10011223

voltage of each device in a circuit, it is possible to plot the relationship and calculate resistance. The initial set up will only yield positive results, limiting the data points to first quadrant of the plot. To obtain negative results and expand the range of data points, one can reverse the direction of the current by switching the connecting wires to the power supply. After fully extending the range of data points on a plot, the slope m can be calculated graphically or by linear regression. The slope can be defined by:

m= IV

As mentioned above, the rearranged Ohm’s law equation is:

R=VI

By comparing the two equations, it becomes clear that the resistance is equivalent to the inverse of the slope.

R= 1m

2.0 Apparatus and Procedure

In the experiment, a circuit will have to be set up using power supply, two multimeters that will function as an ammeter and voltmeter, and a device under test which will provide some sort of resistance to the circuit. The three main parts to the experiment is to measure the resistance of a standard resistor, two light emitting diodes and a traditional light bulb. For safety purposes, the power supply did not exceed a voltage of 12 volts during the lab.

As shown in figure 3, the circuit of the first part is comprised of 390Ω high wattage resistor (R2), the ammeter along the circuit and the voltmeter to measure the change in electrical potential as it passes through the device under test, which is a standard resistor of unknown voltage. Data points were then taken at the max and min to determine the range of the plot (Max occurs when power supply reach 12V and min occur when power supply reaches 12V with reconnected wire (Negative current)). By increasing and decreasing the voltage from max and min, the current and voltage at different points were recorded by the

two multimeters. The data points are then plotted onto a voltage – current plot. Assuming that this is a standard resistor and demonstrate ohmic resistor behaviours, the plot should show a linear relationship

Figure 3: The circuit layout of part 1 (standard resistor) and part 3 (light bulb) of the experiment

Courtesy of APSC 100 Module 2 Manual

Table 1: The recorded voltage and current from 12V to -12V of power supply from the first part of the experiment.

of 13Ian Ip

10011223

in which the slope m is constant and can be determined, which will lead us to the resistance of the unknown resistor by using the equation R=1/m.

The second part of the experiment involve using light emitting diodes (LEDs) as the device under test and placing three 1000Ω resistors in parallel as a collective R2 from part 1. As shown in figure 4, the devices under test are two LEDs in series with one another. Repeat the procedure from part 1 by taking the max and min current and voltage by setting power

supply to 12V and -12V. Note that the low voltages will yield no result because there are no current. It is only after the cut in voltage is reached that increase in current will occur. The cut in voltage is presumed to be the x intercept of the line of best fit from graphical analysis (The cut-in voltage occur when I=0).

The final part of the experiment involves the circuit configuration as shown in figure 3; replace R2 with a 100Ω resistor. Again, repeat the previous procedure and take the max and min values, and then fill the range by recording current and voltage at different data points. In this part of the experiment, qualitative observations of the light bulb should also be recorded to determine as to when the light bulb starts to turn on.

In this experiment, it should be assumed that the multimeters (ammeter and voltmeter) are ideal. Ideal ammeter has no resistance and does not cause a decrease in voltage while ideal voltmeter has infinite resistance so that it draws no current from the circuit. The circuit is to be assembled on a breadboard with the green ground cable attached on one end and grounded on the other end.

3.0 Results and Analysis

The table of values for part 1 of the experiment is as followed:

Figure 4: The circuit layout of part 2 (Light emitting diodes)

Courtesy of APSC 100 Module 2 Manual

of 13Ian Ip

10011223

The first part of the lab made use of an unknown standard resistor and the objective was to calculate the resistance of the unknown resistor by plotting the current as a function of voltage.

As shown in figure 5 and as predicted, the standard resistor demonstrated a linear relationship on the plot and therefore determined to be Ohmic. Further linear regression analysis has confirmed that the R square value is .999957 where 1 is perfect to the regression line and .95 is a good fit, proving that the values are reliable and resemble the line of fit (Refer to the line fit and residual plot in figure 6 and figure 7).

Note that the error of current and voltage varies based on data points and are not constant throughout. Therefore, the error bars have been customized to reflect the changing nature of the uncertainty.

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

-40

-30

-20

-10

0

10

20

30

40

f(x) = 46.4828404584205 x − 0.0033905318052643

Standard ResistorLinear (Standard Resistor)

Voltage (V)

Curr

ent (

mA)

Figure 5: The Voltage and Current Plot of the standard unknown resistor

Figure 6: The Line fit graph of the regression line generated from the data of the unknown standard resistor

Voltage (V)

sV (V) Current (mA)

sI (mA)

-0.66 0.01066 -30.6 0.1018-0.55 0.01055 -25.7 0.0871-0.43 0.01043 -20.1 0.0703-0.32 0.01032 -14.9 0.0547-0.22 0.01022 -10.1 0.0403-0.11 0.01011 -5.2 0.02560.11 0.01011 5.3 0.02590.21 0.01021 9.9 0.03970.32 0.01032 14.7 0.05410.42 0.01042 19.7 0.06910.54 0.01054 25 0.0850.65 0.01065 30.1 0.1003

of 13Ian Ip

10011223

The equation of the line of best fit became known through linear regression and the slope was

revealed to be 46.483. It is known from the above that resistance is product of one thousand and the inverse of the slope. Note that 1000 is the conversion factor from milliamps to amps.

m=46.483

R=

1000 mA1 A

∗1

m

R= 100046.483

R=21.5Ω

Therefore, the resistance of the unknown resistor was determined to be 21.5Ω.

The next part of the lab involves replacing the device under test with LEDs and to determine the cut in voltage of the circuit. As shown in table 2, the data points are exponential in the beginning and ended with linear.

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

-40-30-20-10

010203040

Standard Resistor Line Fit Plot

Current (mA)Predicted Current

Voltage (V)

Y

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

-0.2

-0.1

0

0.1

0.2

Standard Resistor Residual Plot

Voltage (V)

Resid

uals

Figure 7: The Residual plot of the regression line generated from the data of the unknown standard resistor

of 13Ian Ip

10011223

For the purpose of accurate results, the first six data points are omitted from calculation because it occur at low voltage and occur before the expected range of cut in voltage. The expected range of cut in voltage values are based on the visual analysis of the plot, judging on the points that are of the linear portion of the plot. Regression analysis was then performed on this portion of the plot; the equation of the linear portion was determined to be:

I=38.969 V−145.51

Because the cut in voltage occur when I=0, the cut in voltage can also be expressed as the x intercept of the line of best fit of the plot in figure 8.

If I=0, then:V Cut−¿=145.51 /38.969

V Cut−¿=3.73 V

Therefore, the cut in voltage of the LEDs were determined to be 3.73V.

2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.60

5

10

15

20

25

30

f(x) = 38.9688249400479 x − 145.507494004796

LEDsLinear (LEDs)Linear (LEDs)

Voltage (V)

Curr

ent (

mA)

Table 2: The table of values of voltage and current measured from the circuit containing LEDs

Voltage (V)

sV (V) Current (mA)

sI (mA)

3.03 0.01303 0 0.013.44 0.01344 0.1 0.01033.54 0.01354 0.3 0.01093.61 0.01361 0.7 0.01213.66 0.01366 1.2 0.01363.71 0.01371 2 0.0163.8 0.0138 3.8 0.02143.84 0.01384 4.7 0.02413.86 0.01386 5.4 0.02623.9 0.0139 6.6 0.02983.94 0.01394 7.6 0.03283.96 0.01396 8.4 0.03523.99 0.01399 9.6 0.03884.01 0.01401 10.3 0.04094.04 0.01404 11.7 0.04514.08 0.01408 12.7 0.04814.11 0.01411 14.1 0.05234.14 0.01414 15.1 0.05534.17 0.01417 16.8 0.06044.19 0.01419 17.4 0.06224.21 0.01421 18.5 0.06554.25 0.01425 20.2 0.07064.28 0.01428 21.6 0.07484.31 0.01431 22.9 0.07874.35 0.01435 24.6 0.08384.37 0.01437 25.5 0.0865

of 13Ian Ip

10011223

As mentioned before, the resistance of the device(s) under test is given by the following equation:

R=1000/m

In this part of the experiment, the resistance of the LEDs are determined to be:

R=25.7 Ω The resistance of the LEDs was determined to be 25.7Ω.

The third final part of the experiment involves replacing the device under test with a light bulb. Light bulb is typically a non ohmic object and the data recorded in the table of values in table 3 verified the non-linear relationship between current and voltage.

Like previous parts of the lab, a plot was made to demonstrate the current voltage relationship and it was determined that the graph is non-linear and therefore non ohmic (Refer to figure 9).

The resistance was also found to be increasing in both directions as the relationship gets farther and farther away from the origin.

An interesting observation made from the graph shows that the current and voltage is the negative of each of the respected values once the lead to the power supply has been reversed.

The voltage and current at which the light bulb begins to turn on is 2.65V and 30.1mA, as well as the negative counterpart of these two values.

Table 3: The data recorded from the light bulb circuit

Voltage (V)

sV (V) Current (mA)

sI (mA) Resistance, R=V/I (Ohms)

Qualitative state

-7.58 0.01758 -54 0.172 140.3704 Bright-6.99 0.01699 -51.6 0.1648 135.4651 Bright-6.54 0.01654 -49.7 0.1591 131.5895 Medium-6.02 0.01602 -47.4 0.1522 127.0042 Medium-5.59 0.01559 -45.4 0.1462 123.1278 Less Bright-5.01 0.01501 -42.7 0.1381 117.3302 Dim-3.66 0.01366 -35.9 0.1177 101.9499 Very Dim-2.66 0.01266 -30.3 0.1009 87.78878 Almost Off-1.72 0.01172 -24.2 0.0826 71.07438 Off-0.97 0.01097 -18.8 0.0664 51.59574 Off-0.3 0.0103 -12 0.046 25 Off-0.11 0.01011 -6.1 0.0283 18.03279 Off0 0.01 0 0.01 0 Off0.06 0.01006 3.7 0.0211 16.21622 Off0.11 0.01011 6.6 0.0298 16.66667 Off0.19 0.01019 9.1 0.0373 20.87912 Off0.3 0.0103 12.1 0.0463 24.79339 Off0.53 0.01053 15.5 0.0565 34.19355 Off0.87 0.01087 18.1 0.0643 48.0663 Off1.3 0.0113 21.2 0.0736 61.32075 Off1.7 0.0117 24 0.082 70.83333 Off2.17 0.01217 27.2 0.0916 79.77941 Off2.65 0.01265 30.1 0.1003 88.03987 Almost On3.75 0.01375 36.3 0.1189 103.3058 Very Dim4.89 0.01489 42.2 0.1366 115.8768 Dim6.18 0.01618 48.1 0.1543 128.4823 On7.58 0.01758 54 0.172 140.3704 On

of 13Ian Ip

10011223

4.0 Discussion

This lab was conducted without any major hurdles; the only significant challenge encountered was properly assembling the circuit in the beginning. In real world situations, none of the multimeters are ideal but for the purpose of the experiment, it was assumed that the ammeter and voltmeter are ideal. In this experiment, three different devices were tested on resistivity, cut in voltage and the qualitative appearance. The current and voltage data were recorded for each of three devices under test.

The first plot contains the data set of an unknown standard resistor. As expected, the plot demonstrated a linear relationship and the unknown resistor is therefore ohmic. Because it is linear, the slope is a constant that can be calculated and from that, the resistance of the resistor was found. The second plot contains the data set of two LCDs in series with one another. The plot started out as a slow exponential climb that eventually turns into a linear climb just like that of the unknown resistor. The voltage will have to exceed the cut in voltage for the LCDs to demonstrate a linear relationship and hence, ohmic properties. The cut in voltage was found by performing a regression line on the linear portion of the line and determine the x intercept of the line (When I=0), the resistance of the LCD can also be found from the slope of the regression line just as before. The third plot containing the data set of a light bulb in a circuit showed a sideway flipped cubic (y=x^3) relationship.

As current go up, the resistance of the unknown resistor remained constant. The LEDs did something similar but the resistance increased as the current increase prior to reaching the cut in voltage. In the light bulb circuit, resistance increased exponentially as current increases in both positive and negative direction. When reversing the current direction by switching the power supply, it was discovered that the current and voltage is the negative value at the same current and voltage before the current was reversed.

In the light bulb circuit, it was found that the resistance of the filament changes when the bulb heats up. Light bulb as discussed before is a non ohmic resistor and have a non-linear relationship on a current voltage plot. Non-linear relation means the resistance is not constant throughout and poise to change.

-10 -8 -6 -4 -2 0 2 4 6 8 10

-60

-40

-20

0

20

40

60

Light Bulb

Voltage (V)

Curr

ent (

mA)

Figure 9: The current and voltage plot of a light bulb in circuit

of 13Ian Ip

10011223

Data shows the resistance increases as voltage and current increase. As voltage and current increases, the light bulb will naturally get brighter. Since the light bulb is a form of resistor and the electric energy cannot be fully transformed into light energy, the light bulb will also release heat as a form of energy. As the voltage and current increase, so does heat, and therefore further heating up the filament in the bulb. According to the lab manual, it was understood that the resistance of resistors increase as it heats up.

5.0 Conclusion

Overall, this lab was completed in a timely manner and did not encounter any major problems.

In the first part, the resistance of the unknown resistor was determined to be 22 ± 4.5 Ω The LCDs in the second part had a cut in voltage of 3.7 ± 0.15 V The light bulb in the circuit switched on at 2.65V and 30.1mA (as well as the negative of these

values)

6.0 Reference

Clapham, Lynann. APSC 100 Practical Engineering Module 2. Kingston: Queen's University,

2011. Print.

7.0 Appendix

7.1 Error Equations

Voltage:SV =0.001∗|V|+0.01

Current:S I=0.003∗|I|+0.01

Resistance (As a function of Slope, R=1/m)

SR=m∗Sm

Cut in Voltage (As a function of slope and intercept, V=-int/slope)

of 13Ian Ip

10011223

SV Cut−¿=¿

7.2 Unknown Resistor Regression Analysis and Error

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.999978R Square 0.999957Adjusted R Square 0.999952Standard Error 0.141417Observations 12

ANOVA

df SS MS FSignifican

ce F

Regression 1 4612.7094612.70

9230649.

2 3.77E-23

Residual 10 0.1999880.01999

9Total 11 4612.909

Coefficients

Standard Error t Stat P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept -0.00339 0.040825-

0.08305 0.93545 -0.094350.08757

3-

0.094350.08757

3

X Variable 1 46.48284 0.096787480.259

53.77E-

23 46.26719 46.698546.2671

9 46.6985

RESIDUAL OUTPUT

ObservationPredicted

Y Residuals1 -30.6821 0.0820652 -25.569 -0.131053 -19.991 -0.108994 -14.8779 -0.0221

of 13Ian Ip

10011223

5 -10.2296 0.1296156 -5.1165 -0.08357 5.109722 0.1902788 9.758006 0.1419949 14.87112 -0.17112

10 19.5194 0.18059811 25.09734 -0.0973412 30.21046 -0.11046

Error = Slope*Standard Error of SlopeError = 46.48*0.0967

7.3 LCDs Regression Analysis and Error

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.996836R Square 0.993682Adjusted R Square 0.993331Standard Error 0.5596Observations 20

ANOVA

df SS MS FSignifican

ce F

Regression 1886.54

08886.54

082831.0

26 2.98E-21

Residual 185.6367

330.3131

52

Total 19892.17

75

Coefficients

Standard Error t Stat P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

of 13Ian Ip

10011223

Intercept -145.5072.9981

08

-48.533

11.54E-

20 -151.806

-139.20

9

-151.80

6

-139.20

9

X Variable 1 38.968820.7323

9553.207

382.98E-

21 37.4301240.507

5337.430

1240.507

53

Error = ¿

Error = ((145.5/2.998) + (38.968/0.732))*3.7

Error = 0.147

-End

APSC 100 Module 2 Lab 3 - Electrical Resistive Behaviour of Three Devices.docx

Documents

Transcript of APSC 100 Module 2 Lab 3 - Electrical Resistive Behaviour of Three Devices.docx