Homework on Ohm's Law (solutions)

Feel free to work on the homework in groups. The work you hand in, however, should reflect your understanding of the material and be in your own words. Students who turn in identical (or close to identical) homework assignments will be asked to explain their answers orally to the TA or prof. A student who cannot explain how he or she arrived at a given answer will be charged with academic dishonesty.

You should show all of your calculations (neatly) and justify all of your answers for full credit.

A student measured the current through four different objects at five different voltages. Each measurement was then repeated at a higher temperature. The data from this experiment are contained in the table at the bottom of the page. Answer the following questions about this experiment. You should use some quantitative method, such as graphing the data on Excel or a graphing calculator and using a linear fit when necessary, graphing the data carefully by hand and finding a slope from rise over run when necessary, or calculating the resistance of an object for each measurement and looking at its behavior.

The easiest way to begin is by plotting the data (I used a variation of the excel file from class). Room temperature data is plotted with blue diamonds and fit with a dashed line; Higher-temperature data is plotted with pink squares and fit with a solid line.

Object A:

Object B:

Object C:

Object D:

1. Which of the four objects are ohmic (obeys Ohm's law)? How do you know this?
Ohmic devices have a linear relation between current and voltage. Thus they appear as a straight line when plotted on a V vs. i graph. Of the four items here only A and C plot as straight lines. The data points of B and D do not fall on the curve-fit lines shown.

2.
For each of the objects that are ohmic, what is the resistance at room temperature as measured by this experiment? How did you arrive at these numbers?
One can arrive at this by two methods. First, the slope of a V vs. i graph. Excel displays a fitted line and its equation in y = mx+b format. The slope is m, which here is in units of Volts/Ampere or Ohms. The second method would involve finding V / i for each point and then summing and dividing to find the average. For graph A, the slope is 9.94 W; for C, it is 4.69 W.

3. Which of the objects are semiconductors and which are conductors? How did you arrive at this conclusion?
As we discovered in class, semiconductors and conductors behave differently under changes in temperature. Semiconductors require thermal energy to the electrons in the valence band into the conduction band. At higher temperatures the number of charge carriers will increase producing a lower resistance. Conductors, on the other hand, have a valance band which is not full at T=0. Thus, they always have free energy levels within the band to move about in and do not need extra thermal energy to move electrons up in to the conduction band. Instead, increased thermal energy produces more collisions with more energetic particles, inhibiting electron flow and increasing the resistance.
In A and D, the same voltage produces a lower current at room temperature (blue diamonds) than at high temperature (pink squares). Thus they are semiconductors. Items B and C exhibit higher currents at lower temperature, so they are conductors.

Object	At room temperature					At higher temperature
Object	1.0 V	2.0 V	3.0 V	4.0 V	5.0 V	1.0 V	2.0 V	3.0 V	4.0 V	5.0 V
A	0.10 A	0.19 A	0.32 A	0.39 A	0.50 A	0.12 A	0.25 A	0.35 A	0.50 A	0.59 A
B	0.05 A	0.20 A	0.30 A	0.35 A	0.38 A	0.03 A	0.18 A	0.25 A	0.30 A	0.33 A
C	0.20 A	0.38 A	0.62 A	0.83 A	1.04 A	0.18 A	0.39 A	0.57 A	0.80 A	1.00 A
D	0.20 A	0.42 A	0.68 A	1.10 A	1.80 A	0.23 A	0.45 A	0.74 A	1.30 A	2.30 A

1.	Which of the four objects are ohmic (obeys Ohm's law)? How do you know this? Ohmic devices have a linear relation between current and voltage. Thus they appear as a straight line when plotted on a V vs. i graph. Of the four items here only A and C plot as straight lines. The data points of B and D do not fall on the curve-fit lines shown.
2.	For each of the objects that are ohmic, what is the resistance at room temperature as measured by this experiment? How did you arrive at these numbers? One can arrive at this by two methods. First, the slope of a V vs. i graph. Excel displays a fitted line and its equation in y = mx+b format. The slope is m, which here is in units of Volts/Ampere or Ohms. The second method would involve finding V / i for each point and then summing and dividing to find the average. For graph A, the slope is 9.94 W; for C, it is 4.69 W.
3.	Which of the objects are semiconductors and which are conductors? How did you arrive at this conclusion? As we discovered in class, semiconductors and conductors behave differently under changes in temperature. Semiconductors require thermal energy to the electrons in the valence band into the conduction band. At higher temperatures the number of charge carriers will increase producing a lower resistance. Conductors, on the other hand, have a valance band which is not full at T=0. Thus, they always have free energy levels within the band to move about in and do not need extra thermal energy to move electrons up in to the conduction band. Instead, increased thermal energy produces more collisions with more energetic particles, inhibiting electron flow and increasing the resistance. In A and D, the same voltage produces a lower current at room temperature (blue diamonds) than at high temperature (pink squares). Thus they are semiconductors. Items B and C exhibit higher currents at lower temperature, so they are conductors.