PHYS 2426 – Engineering Physics II

Resistance and Ohm’s Law

Leader: _____________________________ Recorder: ___________________________

Skeptic: _____________________________ Encourager: _________________________

Materials

2 x Digital Multimeter (DMM) Calipers, Digital

Analog Ammeter Pasco Circuit Board

6 pieces alligator clip wire Battery Eliminator

Pasco circuit board should include 100 Ω, 330 Ω, and 540 Ω resistors

Wheatstone Bridge Apparatus with slide Laptop

Introduction

In this lab, we will investigate the relationship between current and resistance. For ordinary conductors, we will find that the two are proportional – a result known as Ohm’s Law. Ohm’s Law is named for its discoverer Georg Simon Ohm - a German physicist - who found it experimentally in the early 19^th century. Ohm’s Law is not a law in the sense of Newton’s 2^nd law, but instead is an experimental relationship which works well for certain materials.

Part 1 Resistance

First let us review a result we had in a previous lab we conducted about potential difference.

Q1) When we connected batteries in series, we found that the potential difference of the batteries in series __________

Q2) When we added more batteries in series connected across a light bulb, the light bulb was _________ than if connected across a single battery.

Now, connect a single light bulb in a socket across the Genecon. Turn the Genecon at a rate of about 1 turn per second and observe the brightness of the light bulb and the effort to turn the Genecon.

Next, Use the alligator clip cables to connect two light bulbs in series across the Genecon. Turn the Genecon at a rate of about 1 turn per second.

Q3) Compare the effort required to turn the Genecon now at 1 turn per second to when it was connected across a single light bulb.

Q4) How bright are the light bulbs now compared to before?

Q5) If the brightness of the light bulbs is a measure of the current flowing in the circuit, compare the current flowing in the circuit now compared to when only a single light bulb was connected across the Genecon.

The property of a material which limits current flow through it is called resistance. The greater the resistance of a material, the less current will flow in it.

Q6) When you connect two light bulbs in series, is the resistance of the combination greater, the same, or less than an individual light bulb. Explain your answer.

We can make a circuit schematic to show the circuit we are making. We use a symbol

like to represent a battery or some other source of potential

difference like a Genecon or power supply

and we use to represent a light bulb or a resistor in general. The conducting connections between elements like resistors and batteries we show as straight lines.

Q7) Use the symbols just described to draw a circuit schematic for i) the Genecon connected to one light bulb and ii) the Genecon connected to two light bulbs in series.

We begin to see a by now fairly familiar type of relationship. The more batteries in series, the brighter the bulb (the more current) and the more bulbs in series, the dimmer the bulbs (less current). Batteries are sources of what is called potential difference. A relationship which holds for some materials between current, potential difference, and resistance is called Ohm’s Law, and after familiarizing ourselves with the correct use of voltmeters and ammeters, we will explore Ohm’s Law.

Part 2 Use of Voltmeters and Ammeters

In the following procedure, disconnect your circuits when not making observations to preserve battery life.

Use the Pasco circuit board and connect the two D cells in series and connect the battery across two light bulbs in series. Your circuit should appear something like the following schematic.

Observe the bright ness of the light bulbs, and open the circuit.

When we depict a meter on a schematic we show it by a circle with a letter inside designating the type of meter. Thus a voltmeter will be a circle with a V inside and an ammeter will be a circle with an A inside. Potential differences are measured across objects so when using a voltmeter – or a DMM in voltmeter setting – we place the probes on either side of the object.

Q8) Close the circuit and use the DMM to measure the potential difference across each resistor and record the values. Both values should be positive so reverse the orientation of the leads if you measure a negative value. V₁ = ________ V₂ = __________

Q9) Find the sum of the potential differences

V = V₁ + V₂ = _______

Q10) Measure the potential difference across both resistors and record

V = ________

Q11) How does your answer to Q10) compare to Q9)? Explain why this should be the case.

Q12) Measure the potential difference across the battery and record

V = _______

Q13) How does your answer to Q12) compare to Q9)? Explain why this should be the case.

Now we will find out what happens when we connect a voltmeter incorrectly. Instead of using the voltmeter across a resistor, let us connect it in series with the circuit. Connect the following circuit. Note to put a new element in series, you must make a break in the current circuit.

Q14) What happens to the light bulbs when you place the voltmeter in series with the circuit?

Q15) Does this suggest that a voltmeter has a high resistance or a low resistance? Explain.

Now we will examine using an ammeter. Current flows through a circuit so to measure it, the current must flow through the ammeter. Thus when we use an ammeter correctly it must be placed in series in the circuit.

Remove the voltmeter from the circuit and reconnect the battery across the two light bulbs in series. Take a piece of alligator clip wire and short out one of the light bulbs by connecting the wire from one side of the socket to the other.

Q16) What happens to the other light bulb?

Q17) Did the current increase or decrease when the first light bulb was shorted out?

This is why short circuits are so dangerous. When resistors are shorted out, current can increase by a large amount and this can release a lot of heat and pose a fire danger.

Disconnect the short circuit.

Now we will use an ammeter incorrectly and see what happens. It is very common for people to connect an ammeter like it was a voltmeter, namely to connect it across a circuit element instead of putting it in series with the circuit. Clip one alligator clip lead onto the black common terminal on the ammeter and the other onto the 5 A terminal. This means that the ammeter will read 0 – 5 A. If the lead was connected to the 500 mA terminal it would read 0 – 500 mA and so on. Connect the ammeter across one of the light bulbs and observe what happens. Disconnect once you have made your observation.

Q18) Describe what happens. Did you short out the light bulb?

When you connect an ammeter across a circuit element, you create a short circuit and increase the current in the circuit. This can be dangerous and at the very least can damage the ammeter. Ammeters must be connected in series with the circuit.

Connect the ammeter in series with the light bulbs between the positive terminal of the battery and the first light bulb.

Q19) Are both light bulbs now lit?

Q20) Record the current. Note if the needle seems to be deflecting to the left, reverse the leads to the ammeter.

P21) Do you think it matters where in the circuit you place the ammeter? In other words, if you place the ammeter at different points in the circuit will you read the same thing or different things? Explain.

Connect the ammeter so that it is in series between the two light bulbs.

Q22) Record the current.

Q23) How does the current recorded in Q22) compare the current recorded in Q20)?

Connect the ammeter in series so that it is between the light bulb and the – terminal of the battery.

Q24) Record the current.

Q25) How does the current recorded in Q24) compare the currents recorded in Q20) and Q22)?

Q26) What does your answer to Q25) suggest about the behavior of current in a series circuit?

Q27) Did this agree with the prediction you made in P21) Explain.

Part 3 Ohm’s Law

Introduction

In this experiment we will investigate the relationship between current and potential difference that exists in conductors. This relationship is known as Ohm’s law.

1. Set-Up

Place 100 Ω, 330 Ω, and 540 Ω resistors between empty coils on the Pasco circuit board as shown. Construct the circuit shown below using the 100 Ω resistor. Instead of the batteries, use the battery eliminator as the source of potential difference for this activity. In the circuit diagram the symbol for the potential difference with an arrow drawn through it indicates a variable potential difference.

.

Make sure that the power supply is turned off. Configure a second DMM to be used as an ammeter by plugging one lead into COM and the other into the socket marked 2 A. Connect the ammeter in series with the resistor and connect the other DMM configured as a voltmeter across the resistor. With this arrangement of meters, we will measure the potential across the resistor and the current through it. Before turning on the power supply, check your circuit with the instructor. Incorrect circuits will result in blown fuses and possible damage to the DMM.

2. Using the lowest 5 settings on the power supply, collect and record Voltage versus current data for the 100 Ω resistor. Record your data in a separate, appropriately labeled data table attached to the report.

3. Reverse the leads to the power supply only, so that you apply a negative potential difference across the circuit. Don’t change any of the other connections. Measure and record Voltage (in V) versus Current (in A) for the lowest 5 settings on the power supply.

Add these data to the table you have for the 100 Ω resistor.

4. Repeat both steps 2 and 3 for the two other resistors.

5. Disconnect the circuit and measure the resistance of each of the three resistors for which you recorded data. Record the measured values in your data table. To measure resistance, use the meter with the lead in the V-Ω socket. Place the leads across the resistor (just like measuring potential) and turn to the smallest setting on the Ω scale which gives a reading. Note, if the scale is marked as kΩ, then you need to interpret the reading as having units of kΩ.

Data Analysis

Using Excel or LoggerPro and being sure to include your data for both positive and negative potential differences, construct a graph of Voltage versus Current for each resistor. Answer the following questions.

Q28) For each graph do your data seem to lie along a line?

Q29) Does the line seem to go through the origin? (Or at least very close?)

Q30) What type of relationship is represented by a line that goes through the origin?

Q31) Find the slope of each line. Include the units.

Q32) The resistance is defined as the slop of the graph of V vs. i. For each graph, how does the slope of the line compare to the resistance that you measured for the resistor. Compute the % difference between the value obtained from the slope and the measured value. For our purposes here define the % difference as

Q33). Write an equation for the general relationship shown by your graphs, let V stand for potential difference, i for current and R for resistance. This result is known as Ohm’s Law.

Part 4 Resistivity

Introduction

In this part we will investigate some of the factors which affect the resistance of a piece of metal. In particular we will examine the dependence of the resistance on the length of the metal.

Procedure

1. Connect the 2 D cells on the Pasco circuit board in series and then connect the battery in series with a light bulb and the slide wire Wheatstone Bridge Apparatus (the meter stick with the wire on it.) To connect to the slide wire Wheatstone Bridge apparatus, connect one lead to fixed terminal on one side and connect the other lead to the terminal on the metal piece which slides over the wire as shown below. Move the slide close to the fixed terminal and gently push down on the slide until you make contact with the wire. The light bulb should now light. Move the slide 10 cm away from the fixed terminal and gently press down.

Connect the other lead here

Q34) Is the light bulb brighter or dimmer now?

Q35) What does this suggest about the resistance in the circuit?

Move the slide wire another 10 cm away and repeat.

Q36) Is the light bulb brighter or dimmer now?

Q37) What does this suggest about the resistance in the circuit?

Q38) As we move the slide away from the fixed terminal, we include more of the wire in the circuit. What is happening to the resistance of the circuit as we include more of the wire?

Q39) What type of relationship does this suggest exists between the length of the wire and the resistance? Explain.

2. We will now investigate that relationship. Our apparatus will consist of a DMM and the Wheatstone Bridge Apparatus. Connect the probe connected to the common of the DMM to the connector at the 0 end of the on the Wheatstone Bridge Apparatus. Turn the DMM to the 200 Ω setting. Now, using the other probe measure the resistance of the wire at 10 cm intervals on the meter stick. Record your data of length of wire and corresponding resistance in an appropriately labeled data table attached to the report.

3. Another measurement to make is the following. Remove the common probe from the connector and firmly place the two probes together. Turn the DMM to the most sensitive resistance setting. You should notice that you don’t get 0 Ω as you might expect. The resistance you observe results from the imperfection of the contact between the two probes and is known as contact resistance. Record your contact resistance in your data table as well.

4. Finally, we want to know the cross sectional area of the wire. Use the digital calipers to measure the diameter of the wire and record the value in your data table.

Data Analysis

We will now analyze our data and extract from it the resistivity of the material in the wire. Using Excel or LoggerPro, plot the resistance that you’ve measured vs. the corresponding length of wire. (Remember that it is always y vs. x). Be sure to label your axes with the quantities they represent including units and to give your graph a descriptive title. Add the best-fit line that goes through your data.

Q40) Record the equation of the best fit line.

Q41) Does there seem to be a good linear relationship between the resistance and the length of wire?

Q42) How does the y-intercept of your line compare to the contact resistance you measured earlier?

Q43) If the y-intercept is larger than the contact resistance, what else might contribute to the y-intercept not being zero.

Q44) Complete the following relationship

R ~ _____

A model of the resistance of a piece of metal is given by where R is the resistance, L is the Length, A is the cross sectional area of the metal, and ρ is a constant which depends on the material called the resistivity. From our observation of the contact resistance, we expect that our line probably won’t go exactly through the origin. We modify our model for the measured resistance to

(1) where R_c is the contact resistance.

Q45) Examine equation (1). The slope of the line you’ve found represents the ratio of which physical quantities.

Q46) Assume that the wire has circular cross section and calculate the cross sectional area from the diameter of the wire we measured with the calipers using Remember that radius is given by. Be careful about the units that you use.

Q47) From the value of the slope obtained from your best fit line and the cross sectional area you found, determine the resistivity of the material in the wire. Be sure to include your units. Still be very careful about units.

Q48) Compare your resistivity to a table given in a handbook such as The CRC Handbook of Chemistry and Physics, or else a table that you look up on the web. What do you think the material is in the wire?