# PHYSICS 220/230 Lab 3: Current/Voltage Characteristics and Ohm's Law

Objective:  In this lab we will investigate the current/voltage characteristics of several circuit components. We will also learn various techniques for making measurements of current and voltage in DC circuits.

Background:  Without doubt, the most applied relation in current electricity is that known as Ohm's Law. This principle states that the potential difference or voltage drop V across a circuit component like a conductor is proportional to the electric current I which passes through it, the proportionality constant being defined as the resistance R of the conductor:

V = RI

The unit of resistance is appropriately called the ohm. Thus R is in ohms when V is in volts and I is in amperes. In an electrical circuit with two or more resistances, Ohm's law may be applied to the entire circuit, to a portion of the circuit, or even to each individual resistance of the circuit.

Exercise 1:

Introduction: In this part you will make measurements to determine the resistance of an unknown resistor labeled  in the circuit below as R.

A power supply or battery supplies the applied voltage. A variable resistance inside the power supply allows the output voltage to vary. An ammeter (A) measures the circuit current, and a voltmeter (V) measures the potential difference across the resistance R. Any component in the circuit which does not generate or supply a voltage to the circuit acts like a resistance. This is true for the connecting wires, the ammeter, and the voltmeter. In this circuit, however, the metallic connecting wires have negligibly small resistance so they do not greatly affect the current. An ammeter usually has a negligibly small resistance relative to other resistors that are present.  Also, the voltmeter has a high resistance, so very little current flows through the voltmeter. Hence, to a good approximation, the ammeter reads the current through R as well as through the power supply and its variable resistance. Thus, when applying Ohm's law to the resistance R, V and I are the voltmeter and ammeter readings, respectively.

Procedures:

Make sure all connections are tight and firm. Loose connections make for bad readings and results!  Draw and label a schematic diagram in your lab book.

Wire together the circuit above, paying attention to the proper polarity (+ and -).

• Use the Pasco interface as the variable battery.
• Open DataStudio and "create experiment".  Then double click on "output" in the signal output window.  Choose "DC voltage" from the drop down box and set the voltage to 5v.  Turn off "auto" and turn the generator "on".
•  The positive output is marked with a sine wave and the negative is marked with the symbol for ground.
• The resistor marked A, mounted on the clear plastic board, will be the unknown resistance to be measured.
• The red backed EMD-brand meter will be used as the ammeter. Choose the connection posts marked [-] and [10]. This means that a full-scale reading will be 10 mA, i.e., 10 x 10 -3 Amps. The wiring will have to be reversed at the ammeter if the needle deflection goes negative. Start with the post marked [10] connected to the positive plug on the "battery" and the one marked [-] connected to the resistor.  Before you begin taking data, make sure that the meter reads "0" when no voltage source is present!!
• The FLUKE multimeter will be used as the voltmeter.

Data: Set up the computer using the EXCEL spreadsheet to place corresponding ammeter and voltmeter readings in adjacent columns. Make sure your spreadsheet is well annotated. As you adjust the DC output voltage on the Pasco interface, record both meter readings. Take readings spaced by approximately even amounts for both positive and negative voltages. You should take enough data to illuminate any trends.

Analysis: When your data has been collected, plot V versus I and then run a linear regression on the data. The slope will be a measure of the equivalent resistance R.

Discussion:  For any device which is "ohmic" (obeys Ohm's law), the V-I graph should be linear. Is your resistor "ohmic"? What is the value of R to 90% confidence for resistor A?

Exercise 2:

Introduction: There are circuit devices for which Ohm's law is not an adequate description. Current may depend on voltage in a more complicated way, and the current resulting for a given potential may depend on the polarity of the potential difference. This is the case with "diodes", devices constructed deliberately to conduct much better in one direction than the other.  The circuit symbol for a diode is  .

Procedure: Repeat the procedure from Exercise 1 with a diode in place of the resistor. Put the EMD meter on the 500 mA scale for all your readings.  Hook up the diode with the arrow on its case in the direction of positive current and make sure that the current is less than 300 mA.  Start your readings at 0V and work up and down from that point.

Analysis and Discussion: Graph and print the meter readings V versus I for the diode. Do not do a trendline or a linear fit for the data.  Is the diode ohmic?  Explain.  How does the resistance depend on the direction of current flow?

Exercise 3:

Introduction: The wires used to make your circuits or any electronic device always have some resistance. Knowing how to find the resistance of such wires could be important in determining the characteristics of a circuit or device. One way to determine the resistance of a metal wire is based on the following calculation:

Resistance = (Resistivity of wire) * (Length of wire)/(Cross-sectional area of wire)

Procedure: Using the mounted resistance spools, design and perform an experiment to determine the resistivity of copper wire.  Do not use a current with a magnitude greater than 300 mA and keep the EMD meter on the 500 mA scale for all your readings. Carefully document your procedure (do not just say "like Exercise 1") and present an analysis of your results.  FYI, #22 Gauge copper wire has a diameter of 0.0640 +/- 0.0005 cm.  (Your wire might not be pure copper, however.)  Don't forget to compare your value for the resistivity of copper to the accepted value of 1.7 x 10-8 W-m.  Also, note that the length of wire is labeled on the spool.