L11. Current, Potential Difference, and Resistance in Simple Electric Circuits

Before you start:  Complete the tutorial on how to use a multimeter to measure voltages, currents, and resistances.

About working together:  You may share equipment with one other student for this lab. However, each person must connect their own circuits and make their own measurements. This is the only way you will learn to connect electrical circuits and use the multimeter.

About your report: You'll submit data and analysis for this lab in a Graphical Analysis file.  As you take data, record it on notebook paper.  You can transfer to the GA file later.

Goal:  To determine the relationship between a) current and potential difference, and b) current and resistance for simple resistors.

Equipment

Multimeter or individual voltmeter and ammeter
Selection of resistors from 500 to 10,000 W
4 to 6 1.5-V batteries
Battery holders for 1, 2, and 4 batteries (or strong tape to hold batteries together)
3-4 alligator clip wires

You may use a breadboard for making connections if you have one available.

Introduction

In this lab you’ll investigate the behavior of the electric current in a simple circuit.  A simple circuit is one that contains only one resistor and a battery or a series of batteries connected in a chain. You can select different battery voltages by combining single batteries in a circuit. You’ll select resistors in the range of 500 to 10,000 W . You’ll have a multimeter to measure voltages, currents, and resistances, and you’ll have wires to connect the components.

Note that it's common practice to use the word voltage to mean potential difference.  Therefore, these terms may be used interchangeably.

Hints for taking, recording, and displaying data

As you know, the color code on resistors doesn't necessarily provide an accurate value of the resistance.  Therefore, use the resistance measurement function on the multimeter (if you have one) in order to get the best values.  If you don't have a way to measure resistance, you'll have to use the color code, but you can expect greater errors.

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 all data.   Students frequently forget to record the value of the resistance for Part A and the value of the battery voltage for Part B.

Since you're looking for relationships between current, potential difference, and resistance, you'll need to draw graphs and fit them to functions.  Use what you know from your reading to select functions that match the physics that you expect.  In order to get good results, you'll need a sufficient quantity of data.  At least 5 data points per investigation are recommended. 

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.

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

In this investigation, 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.  If you're using battery holders, the holder automatically connects the batteries that way.  If you don't have holders, tape the batteries together securely with the positive terminal of one touching the negative terminal of the next.  For standard AA, C, and D batteries, the positive terminal is the one sticking out.  The negative terminal is the other end of the battery.  These are usually marked.  A complete circuit with 3 batteries in series with a resistor is shown.

If you have 5 batteries, you can get values of voltage from about 1.5 to 7.5 V.  For each different number of batteries, measure the voltage across the resistor.  That would be V_DC in the diagram.  Note that you could also measure V_BA and get the same result as V_DC within a few tenths of an volt.  (Why is that?)  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 (dial and red probe to V or A).  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.

Once you have your data, go on to Part B.  Leave the analysis for later.

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.  We recommend at least four, because the currents will be small when the resistances are large.  For whatever number of batteries you use, don't forget to 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.  You should have 4 different values of resistance, but 5 or 6 are better.  (Three of the resistors sent to you have about the same value. You wouldn't, for example, consider 993 and 1010 W to be different values.  They're too close to the same.)  You can obtain additional values by connecting resistors in series (a chain).  You should have already measured the values of the individual resistances in the tutorial.  When you use resistors in series, you'll need to measure the resistance between the two ends of the chain.  Remember not to have the batteries in the circuit when you measure resistance. 

Measure the current for each resistance value by opening the circuit in the usual way.

Turn off your meter and disconnect the circuit when you have your data.  Then go on to the analysis.

You have much experience by now in using graphs to find relationships.  You know how to display data, label variables, select appropriate fits, make matching tables, and write physics equations corresponding to the fit equations.  We expect you to do those things in your analysis without being given step-by-step instructions.  One thing that some people have been doing is leaving units off of fit coefficients and displaying matching tables incompletely.  See Lab FAQ to review.

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 Graphical Analysis. (See note below.) Label all pages with descriptive names (The default names of Page 1, Page 2, etc. are unacceptable.)  Do the same for graphs.  Use the text box on each page to show your matching table and other calculations that you do related to the analysis.  You'll also need to give the value of the constants for each part.  In Part A, the constant was the resistance.  What was the constant in Part B?

Note 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.

Note about selecting curve fits: If you expect the relationship to be linear, select a linear fit rather than a proportional fit. That way you don't force the fit through the origin, which need not represent actual data. If you expect the relationship to be inverse, you could select an inverse function, but a better way is to re-express one of the variables as its reciprocal. Then apply a linear fit.

Once you have the equations of fit for each part, you can compare to the expected physics equation.  You can use the fit coefficients as a check on your work.  For example, in Part A, we're expecting that you'll have a linear fit.  The slope of that fit has a relationship to the resistance that you used.  You should determine if the slope has the value that would be expected based on the resistance that you used.  A similar consideration will apply to one of the fit coefficients in Part B.

On a third page of your GA file, summarize the methods you used to work toward achieving the goals of the experiment.  Give your results and discuss differences and similarities with expected results.  Discuss possible sources of error qualitatively.

Submitting your work

Name your GA file the usual way and submit it by the due date as instructed.