OHM’S LAW
key words: current, electromotive force, resistance, resistor

INTRODUCTION
During the nineteenth century so many advances were made in understanding the electrical nature of matter that it has been called the “age of electricity.” One such advance was made by an investigator named Georg Simon Ohm. Ohm was interested in examining the relative conductivity of metals and in investigating the relationship between the electromotive force (potential difference) and the current in a conductor.

By taking wires made from different materials but having the same thickness, passing a current through these wires and measuring the electromotive force (i.e., the potential difference between the ends of the conducting wire), he was able to experimentally determine the relative conductivity of certain metals such as silver, copper, and gold.

In another experiment using a piece of apparatus that he built himself, Ohm investigated the effect of current in a conductor on the voltage drop across the conductor. He found that for a given conductor the voltage drop was directly proportional to the current in the wire. When voltage is plotted against the current in a given conductor, the data can be fitted to a straight line, the slope of which is the resistance of the conductor. This result was published in 1826. In recognition of Ohm’s work, this empirical relationship bears his name.

DISCUSSION OF PRINCIPLES
Ohm’s Law can be written algebraically as V = RI, where V represents the potential drop across the conductor (measured in volts), I the current in the conductor (measured in amperes), and R the resistance of the conductor measured in units called “ohms” (symbolized by Ω, upper-case Greek omega).

Resistance and Resistors
Resistance is a property of materials. Resistors are conducting devices made from materials which satisfy Ohm’s Law.

If the potential difference across a resistor is set at 1 volt, and if a current of 1 amp is measured in the conductor, then its resistance is determined to be 1 ohm, or 1W. Instead of using thin wires as Ohm did in his original experiment, you will replicate his results using small cylindrical ceramic resistors. You will notice colored bands on the resistors. These bands form a code that indicates the resistance of the resistor. Later in this experiment you will learn how to read this color code.

Combinations of Resistors
Resistors can be combined in simple circuit arrangements that increase or decrease the overall resistance in the circuit. These arrangements are called series and parallel circuits. Figure 1(a) illustrates two resistors connected in series and Figure 1(b) shows the resistors in a parallel arrangement.

Figure 1 Resistors in Series and Parallel Arrangements

In order for charges to move in a conductor, there must be a potential difference across the conductor. In order for charges to move through a circuit, there must be a complete path leading away from and back to the source of emf (V_AB in Figure 1).

As you can see, in the series arrangement shown in Figure 1(a) the current in the circuit goes through each resistor. If we compute the potential drop V₁ across R₁ using Ohm’s Law, it is merely V₁ = IR₁. Likewise, the drop across R₂ is V₂ = IR₂. The potential drop across both resistors is V_AB = V₁ + V₂. One can think of the applied voltage V_AB being divided between the two series resistors R₁ and R₂.

In the parallel arrangement shown in Figure 1(b), however, the current can divide at the junction A and recombine at junction B. Therefore, the current through R₁ and R₂ may be different. Notice that in this case V_AB = V₁ = V₂. That is, the potential drop across each resistor is the same.

Using some simple algebra and your understanding of the potential drops in a simple series or parallel circuit, the relationships for determining equivalent resistance for resistors in series and/or parallel can be derived. These relationships are:

(The equivalent resistance is simply the sum of the individual resistances.)

(The reciprocal of the equivalent resistance is the sum of the reciprocals of the individual resistances.)

As suggested in Eqs. (1) and (2), the sums include a term for each resistor in the circuit.

PROCEDURE (A):
Determining Resistance
We will use a computer and software to act as our battery and voltmeter, while we will monitor the current with a hand-held multimeter. Do not turn on the power to your circuit until your lab instructor has checked your wiring.

1.) Turn on the computer and monitor, the Interface Device, and the Power Amplifier.

1. Plug the rear output of the Power Amplifier into Analog Channel C of the Interface.

2. Plug a voltage probe into Analog Channel A of the Signal Interface.

2.) Open the folder “LABS” by double clicking on the folder if it is not already open. Once the Labs folder is open, open the “Ohm’s Law” file. The file should open to look like that shown in Figure 2 below. The window shows both a digital and analog voltmeter, both measuring the voltage from the voltage probe.

Figure 2 Start-up screen

3.) Connect the circuit shown in Figure 3, using the resistor labeled as “100 W” on the circuit board. We will use a small multimeter as an ammeter. Set the multimeter to the range marked 2 DCA.

Figure 3 Circuit Diagram for Procedure A

Our “voltmeter” is actually our computer connected to the Signal Interface. Voltmeters have a relatively high resistance and are placed in parallel with the resistor. Ammeters, with their relatively low resistance, are placed in series with the resistor.

4.) Select the Signal Generator window by clicking in that window. The Signal Generator window is shown in Figure 4. Turn on the signal generator by clicking on the ON button. Click the DC button if it is not already highlighted. Set the DC voltage to 1 V by clicking on the small up arrow next to the voltage setting.

Figure 4 Signal Generator Window

5.) Press Command M to start taking data. With R₁ in the circuit, obtain six current and voltage measurements by increasing the voltage in 1-volt steps. Record this information in the data table below.

6.) Construct a graph of voltage versus current.

Resistance 1 = _________________ ohm (Measured)

Reading the resistor code
The resistance of most ceramic resistors can be determined from the colored bands printed on the resistor. Each color represents a digit from 0 to 9.

Resistance 1 = __________ ± _____ ohm (color code)

9.) Compute a percent error between the accepted value of the resistance and the measured value.

Percent error = _________________ %

10.) Switch the wires on the circuit board so that you will measure the resistor marked 33 W in the circuit shown in Figure 3. By making one measurement of voltage and current, compute the resistance for this resistor. Determine the percent error between the labeled value and the measured value.

Resistance 2 = _________________ ohm (Measured)

Percent error = _________________ %

Does your measured resistance value agree with the expected value within the manufactured tolerance?

PROCEDURE (B)
Determining Equivalent Resistance: Series Arrangement
11.) Connect the two resistors you used before in a series arrangement. Measure the equivalent resistance of the circuit by the same method you just used for the 33-W resistor.

Voltage = __________ volt R_equivalent = __________ ohm (Measured)

Current = __________ amp

Compute the theoretical equivalent resistance using Eq. (1), the formula for calculating equivalent resistance for resistors connected in series, and the values given by the color-code bands.

R_equivalent = __________ ohm (Theoretical)


Compute the percent error between the measured and calculated value.

Percent error = _________________ %


PROCEDURE (C):
Determining Equivalent Resistance: Parallel Arrangement
12.) Connect your two resistors in a parallel arrangement. Measure the voltage and current as in Procedure (B), and compute the equivalent resistance of the circuit.

Voltage = __________ volt R_equivalent = __________ ohm (Measured)

Current = __________ amp

Compute the theoretical equivalent resistance using Eq. (2), the formula for calculating equivalent resistance for resistors connected in a parallel, and determine the percent error.

R_equivalent = __________ ohm (Theoretical)


Percent error = _________________ %


QUESTIONS FOR DISCUSSION

1. Do your experimental results verify Ohm’s Law? Explain.

2. Showing all steps, derive Eq. (1), the relationship for the equivalent resistance for a series arrangement.

3. Showing all steps, derive Eq. (2), the relationship for the equivalent resistance for a parallel arrangement.

4. Suppose you wish to determine the resistance of an unmarked resistor. If the only equipment you have is a power supply, a voltmeter and a known resistor R₀, how would you determine the unknown resistance?

5. Explain why a voltmeter is placed in parallel with a resistor. To answer this questions, expand on the information given in the lab manual using the physical concepts that you learned in this lab.

6. Explain in detail why an ammeter is placed in series with a resistor.

7. Determine the resistance of each resistor with the following color code:

1. Red - Black - Brown

2. Gray - Orange - Orange

3. Black - White - Yellow

4. Green - Blue - Brown

8. Three resistors, R₁ = 1500 ohms, R₂ = 150 ohms, and R₃ = 1000 ohms, are connected in series. Calculate the equivalent resistance.

9. What is the equivalent resistance if the resistors in question #8 are placed in parallel with one another?

10. Suppose three identical lamps are connected in series to one another. If the filament of one of the lamps burns out, what happens to the other lamps?

11. Suppose three identical lamps are connected in parallel. If the filament of one of the lamps burns out, what happens to the other lamps?

12. Compare the current in a light bulb connected to a 220-volt source to the current in the bulb when connected to a 110-volt source.