Lab 4: Current/Voltage Characteristics and Ohm's Law

Object:

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 or to a portion or even to
each individual resistance of the circuit.

Consider the following simple circuit:

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 and the ammeter have
negligibly small resistance so they do not greatly affect the current. 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.

Experimental Procedure:

Make sure all connections are tight and firm. Loose connections make for bad readings and results!

**For each circuit, draw and label a schematic diagram in your lab book!**

Wire together the above circuit; pay attention to the proper polarity (+ and -). You will use the function generator as a variable battery. You should push in the DC Offset pushbutton and keep the amplitude knob turned all the way off, i.e., fully counterclockwise. The Amplitude Control is the inner shaft of a dual concentric control. The outer ring on the same shaft is the DC Offset control and it will be used to vary the voltage. You can avoid having the amplitude setting slip by always starting with the Offset Control fully clockwise and the Amplitude Control fully counterclockwise. Then any counterclockwise movement of the Offset ring will decrease the voltage output but will not change the Amplitude knob position. The positive output on the generator is marked Hi and the negative is marked Gnd.

A resistor marked A and mounted on a small masonite board will be the first 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 deflection goes
negative. Start with the post marked [10] connected to the Hi plug on the
"battery" and the one marked [-] connected to the resistor.

The METEX multimeter will be used as the voltmeter. Choose a scale setting with a maximum of 20 V DC.

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 Offset outer ring settings on the function generator, record both meter readings. Take readings spaced by approximately even amounts for both positive and negative voltages, say increments of 1 volt or less. Remember that if you rotate the ring clockwise then hold the inner shaft control so it does not rotate.

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**.
For any device which is "ohmic" (obeys Ohm's law), the graph should be linear
with a constant slope. Is your resistor "ohmic"? What is the value of R to 90%
confidence for resistor A?

There are other ways to measure current and voltage. Since an ammeter is configured so that it has a small resistance and thus very little effect on the circuit, you could just as well use a small known resistor in the circuit and measure the voltage across the resistor. Then you would convert your readings to current values using Ohm's Law. You can also use the Pasco Science Workshop Interface to measure the voltage across the small known resistor or any other resistor. To use the Pasco Interface, remember to click on: PY Software, Science Workshop, and Sciwkshp.exe.

In order to measure the resistance of resistor B, make a series circuit with the
battery as your power supply, the standard wire resistor as your current measuring device,
the switch and resistor B. Use the computer to measure the voltage across the wire
resistor. Use the METEX multimeter set to 2V DC to measure the voltage across the unknown
resistor B. Since you are not varying the voltage of the battery, you will not need to use
the spreadsheet or use a linear regression. On the Science Workshop screen, set up an
analog voltage sensor plug in Channel A and use digits for the display icon. Double click
on the voltage window and set the number of right digits to four. Then, double click on
the lightning bolt icon below Channel A and set the sensitivity to HIGH (100X). WARNING:
the input voltage range is now -0.1V to 0.1V. DO NOT EXCEED THIS RANGE.

Close the switch only when you want to take your readings. Once you have your two voltage
readings determine the current in the circuit and the resistance value for resistor B.

The voltmeter ideally should have no effect on the circuit. That is why the METEX
voltmeter has an input "impedance" of 20 M Ohm. To simulate the effect of a
voltmeter with a lower resistance, add the 20 k Ohm resistance in parallel with resistor
B. Then measure the voltage across B and the wire resistor and determine the current in
the circuit. What is the overall effect of this lower impedance "voltmeter"?

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.

Repeat the procedure from Part 1 with a diode in place of the resistor but do not
include a linear regression for all the data. Hook up the diode with the arrow on its case
in the direction of positive current with the voltage at its maximum positive value. The
recorded meter readings should be evenly spaced in __current__ and closer together than
above. Graph and print the meter readings **V** versus **I** for the diode. By
using only the positive voltages, use LINEST to determine the slope of the graph. Using
only negative voltages down to -1 V, determine the slope of the graph. How do you
interpret these results in terms of the effect of the diode on the circuit?

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. According to your textbook, the 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)

Use the circuit in Part 1 with the battery as your power supply and the mounted resistance spools as your resistors. Connect wires to the resistance spool with the spade lugs and include the switch in your circuit. Use the [100] and [-] terminals on your ammeter and the appropriate scale on your voltmeter. Find the resistance of spool A by measuring the current through the circuit and the voltage across the spool. From the resistance and the known length and cross-sectional area, determine the resistivity of the copper wire. #22 Gauge wire has a diameter of 0.06438 cm. Compare your measured resistivity to the known value.

Then, find the resistance of spool E and determine the resistivity of the Nickel-Silver wire. This is an unknown and we will use values from the class to determine this parameter.