# Ohm's Law

A lab report on this lab is due next week.

### Introduction

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance between them.

The mathematical equation that describes this relationship is

V = IR (1)

where V is the voltage (or potential) measured in volts (v), R is the resistance measured in Ohms (Ω), and I is the current measured in amperes. If the resistance is constant over a large range of values of current and voltage, the resistor is referred to as an ohmic device. In this experiment, you will examine the relationship between current and voltage in both ohmic (ceramic resistors) and non-ohmic (ie: a light bulb) devices.

This lab also examines the effect of placing resistors in series and parallel with each other. Placing resistors in series should have the effect of increasing the total resistance, as predicted by the following formula:

R_{Total} = R_{1} + R_{2} + ... (2)

Placing resistors in parallel should have the effect of decreasing the total resistance, as predicted by the following formula:

1/R_{Total} = 1/R_{1} + 1/R_{2} + ... (3)

### Objectives

- To examine the effect on total resistance of placing resistors in series and parallel
- To examine the differences between ohmic and non-ohmic devices

### Materials

- 4-Battery pack or variable power supply
- Alligator wires
- Various Resistors
- Multimeters for voltage and current

### Activity 1 – Measuring resistance with a multimeter

On your table are two different ceramic resistors, in blue containers labeled A and B. Make sure that they are not connected to any circuit, especially to a power supply. Dial your volt/ohm multimeter to the resistance range, then place the probes across the terminals of the eachresistor. Record the resistance of each. Include your uncertainty.

### Activity 2 – Graphically determining resistance

The purpose of this activity is to graphically determine the resistance of two ohmic resistors. If they are ohmic, then the resistance should remain constant over a wide range of voltages and currents.

Draw the circuit diagram using the symbols below.

Figure 1: Measuring Voltage and Current in a Simple Circuit (the block is a resistor)

The above circuit will allow you to simultaneously measure the current through, and the voltage across, a resistor connected to the battery pack. In Figure 1, the resistor is represented by the rectangular block. The "A" represents the ammeter, and the "V" represents the voltmeter. The symbol with the long and short line represents the battery pack.

Notice that the ammeter is in series with the other components of the electric circuit. The voltmeter, however, will be placed in parallel using the black and red probes. Your ammeter reads in units of mA. The current in your circuit should never exceed 200 mA, or 0.2 A. Your volt meter reads in units of volts. If your voltmeter has a range setting, set it to the 20 V range.

Using Resistor "A," construct your circuit, but do not connect to the battery pack yet. Before you can connect to the batteries, you must get affirmation from your laboratory instructor.

Note that the 4-battery pack has notches cut out where the batteries meet. There is a Fahnestock clip that fits into the notch and between batteries. By inserting the clip between the first and second battery (going from negative to positive), and then connecting the rest of your circuit to that clip, you are effectively bypassing the other three batteries.

By moving your clip from one notch to the next, you are now including the next battery in the circuit. This second battery is now in series with the first battery, which results in an increase in the circuit voltage. As the voltage across the resistor changes, the current through the resistor will also change.

With a 4-battery pack, you should be able acquire up to five ordered pair of voltage and current (zero volts and zero current count as valid data point). Measure these values using multimeters, and record these values in a table in your notebook. Don't forget to include your uncertainty!

1) No battery

2) One battery

3) Two batteries in series

4) Three batteries in series

5) Four batteries in series

If you are using a variable power supply instead of a 4-battery pack, draw your voltage from the terminals on the right side of the power supply. Before connecting your circuit, make sure that the voltage knob is turned all the way down (counter-clockwise). You may then turn the knob to generate different voltages. However, to keep yourself and the equiment safe, make sure that the voltage NEVER exceeds 10 V.

If the resistor is "ohmic" (meaning that the resistance remains constant through a wide range of voltages), Ohm's Law (Eq. 1) becomes a linear equation in the form y = mx where the variables y and x are voltage and current.

Your task is to build a data set of the variables (voltage and current) that you can model with a linear fit in Excel. From that linear fit, you will determine the value of the resistor.

Create a graph in Excel that will allow you to determine the value of your resistor.

Compare this value to the value you measured in Activity 1, using percent difference.

Repeat this activity using Resistor B. You must rotate lab partners so that a new person gets to use the computer, and a new person also gets to build the circuit and make measurements.

### Activity 3 – Series Resistors

Using the resistances of A and B that you measured in Activity 1, use Eq. (2) to predict the total theoretical resistance of these resistors if they were connected in series.

Draw the diagram of a circuit that will allow you to measure the voltage across and the current through two resistors in series.

Consctruct this circuit, but do not connect the battery until your laboratory instructor has given you permission.

Connect all 4 batteries across the series combination. Measure the voltage across and the current through the series combination. Use these values to calculate the total resistance.

Using percent difference, compare your graphically determined series resistance to your predicted value.

### Activity 4 – Parallel Resistors

Using the resistances of A and B that you measured in Activity 1, use Eq. (3) to predict the total theoretical resistance of these resistors if they were connected in parallel.

Draw the diagram of a circuit that will allow you to measure the voltage across and the current through two resistors in parallel.

Consctruct this circuit, but do not connect the battery until your laboratory instructor has given you permission.

Connect all 4 batteries across the parallel combination. Measure the voltage across and the current through the series combination. Use these values to calculate the total resistance.

Using percent difference, compare your graphically determined parallel resistance to your predicted value.

### Activity 5 – A Non-Ohmic Device

Repeat Activity 2 using a low-voltage lamp. Plot this data set on a new graph. Show that the resulting curve is more quadratic than linear (Hint: Fit both types of curve to the same data. You can show more than one curve fit for a data set).

According to your graph, how does the resistance of a lamp change as the current and voltage increase?

### Post-lab Questions

Please show all your work for credit. You will not receive credit for just writing the answer without showing all the steps and equations. Untidy work will not be graded.

1) For a particular resistor, you measure a current of 224 mA when the voltage across the resistor is 3.02 V. What do you predict the current will be when the voltage is decreased to 2.34 V?

2) You have determined that two resistors have resitances of 294 Ohms and 326 Ohms. What do you predict will be the total resistance when you put these resistors in series?

3) You have determined that two resistors have resitances of 294 Ohms and 326 Ohms. What do you predict will be the total resistance when you put these resistors in parallel?

4) For a particular resistor, you measure a current of 312 mA and a voltage of 5.93 V. What is the resistance of the resistor?

5) For a particular resistor, you measure a current of 312 mA and a voltage of 5.93 V. When you decrease the voltage to 3.02 V, you measure a current of 224 mA. Is this an ohmic device? Why or why not?