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 L161. Current, Potential Difference, and Resistance in Single Loop Circuits

Goal

To determine the relationship between a) current and potential difference, and b) current and resistance for carbon resistors

Prerequisites

1. Successfully complete L159. (This includes retaking data and revising the analysis if requested by the instructor.)
3. Complete L161PL.

1. Download and print this recording form. Record original data and other information on this form.
2. You'll enter your data for checking by the teacher in WA L161D.
3. You'll submit your LP analysis file to WA L161.

Equipment

• Multimeter
• Selection of carbon resistors from 470 to 10,000 Ω
• 4 1.5-V batteries
• Battery holders (Type I or II)
• 4 alligator clip wires

Introduction

A single loop circuit is one that has only one path for the current. In a previous lab (L159), you investigated the relationship of current to voltage for a light bulb in a single loop circuit. In the present lab, you'll investigate relationships between current, voltage, and resistance for carbon resistors in single loop circuits. These resistors are commonly used in electrical circuits and do not typically get hot like incandescent light bulbs must do to give off visible light. That, together with the fact that the temperature coefficient of resistivity of carbon is much smaller than that of tungsten means that carbon resistors obey Ohm's Law in normal operation. You’ll select several of these resistors in the range of 500 to 10,000 Ω . You’ll use your multimeter to measure potential differences, currents, and resistances in single loop circuits.

 Notes about data collection and recording The color code on resistors doesn't necessarily provide an accurate value of the resistance. Therefore, use the resistance measurement function on the multimeter in order to get the most accurate values.  Likewise, don't assume that a 1.5-V battery actually has a 1.5-V potential difference across its terminals. That value changes as the battery weakens. Therefore, always measure the potential difference using the meter. Record data in SI units. Record all data. Students sometimes forget to record the value of the resistance for Part A and the value of the battery voltage for Part B.

Part A. Current as a function of potential difference (or voltage)

In this part, you'll determine the relationship between the current in a resistor and the potential difference across it. (Note the terminology, current in and potential difference across. Avoid using phrases such as potential difference in or through, as these are, strictly speaking, incorrect.)  The independent variable is the battery voltage. You obtain different values of battery voltage by connecting different numbers of batteries in series. A series connection is one where the batteries are connected + to - in a chain. When using theType I battery holder (Figure 1), it automatically connects the batteries in series.

Now on to making a circuit. A complete circuit with 3 batteries in series with a resistor is shown below.

With your battery holder(s), you can obtain 4 values of voltage from about 1.5 to 6 V. For each different number of batteries, measure the voltage across the resistor. Remember to put the positive (red) probe on point B, the point nearest the positive terminal of the battery. In this way, your readings will be positive. You also need to measure the current. You can open the circuit at any of the points A, B, C, or D in order to measure current. Since you'll be switching between measuring voltage and current as you change the number of batteries, you'll need to be especially watchful to make the necessary changes on the meter. These include changing the placement of the red probe as well as the position of the dial. Alternatively, you could measure all the voltages first, adding the batteries one at a time. Then you could remove the batteries one at a time and measure the currents. If you use this method, take measurements quickly, since the batteries will weaken the longer they're connected to a resistor.

1. Record your data in the WebAssign form L161D. It will include a table like the one below. Note that you'll record current in amperes. If the meter reads in milliamperes, don't forget to convert to amperes before recording the measurement. Remember also that what you write in the table (resistance, potential difference, current) are the measurements you make with the meter. It would be incorrect to, say, write 1.5, 3.0, etc. for the potential differences of the batteries. For the resistor, use one of the resistors with the color code brown-black-red. (Be careful not to use the brown-black-orange resistor.) Turn off your meter and disconnect the circuit when you have your data.
 Part A. Data Resistance (Ω) = <_> No. of batteries Voltage across resistor (V) Current in resistor, I ( A ) 1 <_> <_> 2 <_> <_> 3 <_> <_> 4 <_> <_>

Notify the teacher when you've submitted item 1 of L161D. Wait for a response before continuing with Part B.

Part B. Current as a function of resistance

In this investigation, you'll determine the relationship between the current in a resistor and the value of the resistance. You'll keep the number of batteries constant. Use all 4 batteries, because the currents will be small when the resistances are large. Remember to measure and record the potential difference across the chain of batteries. You'll need this value later.

The independent variable is the resistance, so you'll be using different resistors. Use 5 different values of resistance from 470 to 10,000 Ω. Some of the resistors sent to you have about the same value. You wouldn't, for example, consider 993 and 1010 Ω to be different values. They're too close to the same. Do not use the 10 and 100 Ω resistors.

1. The WebAssign form includes a table like the one below. Measure and record the potential difference across the battery pack. Next measure the resistance of each of the resistors with the meter and enter values in the table. Then connect each resistor into the circuit in turn and measure the current. Turn off your meter and disconnect the circuit when you have your data.
 Part B. Data Potential difference of battery pack (V) = <_> Resistance (Ω) Current, I (A) <_> <_> <_> <_> <_> <_> <_> <_> <_> <_>

Notify the teacher when you've submitted item 2 of L161D. Wait for a response before continuing with the analysis.

Analysis

 Notes about graphical analysis Use SI units in your tables and graphs. Mixing amperes and milliamperes is a common reason for powers of ten mistakes in this lab. Current is the dependent variable in both of the investigations. It's standard practice to plot the dependent variable on the y-axis. Use this convention. Since you're looking for relationships between current, potential difference, and resistance, you'll need to draw graphs and, in one case, to re-express a variable in order to get a linear relationship. Use what you know from your reading to make choices consistent with the physics that you expect.

You'll have an analysis for Part A and another for Part B. Display the data, graph, and fit for each of these investigations on a different page of Logger Pro. (See note below.) Label all pages with descriptive names. Do the same for graphs.

About entering multiple data sets: After you've entered the data for Part A, here's how to add data for Part B. Select Data, New Data Set Two new columns will be added to your data table. You can rename these and enter data independently of your first set. On two different pages of your file, you can plot and fit different data sets.

About re-expressing variables: For one of the data sets, you'll need to re-express a variable in order to produce a linear fit. Use physics judgement to decide on the form of the re-expression. Your physics judgement comes from the theory that you've studied in the textbook.

Provide the following information in a textbox for each fit:

1. Matching table. There will be expected values for slope and intercept.

2. Equation of the fit

3. Explanation in words of how you decided on the expected values for the slope and intercept of your linearized graph

4. Calculation of the experimental error between the fit and expected values of the slope. Use the expected value as accepted.

Discussion of Error and Conclusion

Write these sections on a third page of your Logger Pro file.

For the Discussion of Error, it's sufficient to do a qualitative discussion of two potential sources of error.

Divide the Conclusion into a Part A and a Part B. For each part, describe the method of analysis and give the results. You need not describe the method by which measurements were taken, as that was part of the prelab.