Ohm's Law Lab

Electrical Resistance

and Ohm’s Law UM Physics Demo Lab 07/2013

Pre-Lab Question

For a given potential difference (voltage), does the current in a circuit increase or decrease as the resistance of a circuit increases?

EXPLORATION

Materials

1 green multimeter (with leads)

1 battery board

1 alligator lead card

1 resistor

1 calculator

1 clear plastic ruler

1. Direct Measurement of Resistance

Take the resistor and measure its resistance with the multimeter set to Ω. The Greek letter omega (Ω) is the symbol for Ohms, the unit of resistance.

You measure resistance across a resistor, just as you measure voltage, but using the Ω scale on the multimeter.

Resistance of Resistor: ______

2. Voltage Versus Current for a Resistor

Build a series circuit with 4 cells in series (a 6V battery), a switch, and the resistor that you just measured connected with alligator leads. Measure the voltage and current of the circuit with different applied voltages.

Make it easy on yourself: Measure the voltage first. Connect the multimeter across the resistor, and change the applied voltage from the battery by moving one alligator lead to include fewer and fewer cells in the circuit. Record your findings in the table on the following page.

Second, complete the current measurements. This time, interrupt the circuit with the multimeter and measure in mA. Again change the applied voltage from the batteries by moving one alligator lead for each measurement. Record your findings in the table below.

Number of Cells / Potential (Volts) / Current (mA) / Current (A)
4
3
2
1
0

Plot a graph with the values for voltage and current you found. Plot the potential in volts on the vertical axis and the current in Amperes (Note: you measured current in milliamperes) on the horizontal axis.

What is the shape of the graph? What is the relationship between voltage, current, and resistance? What quantity derived from your graph characterizes the resistance of the resistor? (Hint: one Ohm of resistance is one Volt per Ampere: 1Ω = (1V)/A ).

3. Voltage Versus Current for a Light Bulb

Remove the resistor from the circuit and replace it with a light bulb. Do not measure the resistance with the multimeter. Repeat your measurements of voltage and current with different numbers of cells.

Number of Cells / Potential (Volts) / Current (mA) / Current (A)
4
3
2
1
0

Plot a graph with the values for the voltages and currents you measured for the light bulb.

Find the resistance of the light bulb from the data you measured.

Measure the resistance of the light bulb with the multimeter: ______

Compare the plot for the light bulb with the graph for your resistor measurements. Do the graphs have the same shape? Does the resistance measured from the graph for the light bulb agree with the multimeter measurement of the light bulb’s resistance? What effect might account for the light bulb’s behavior?

Everyday Applications

Simple resistors are used in many everyday appliances:

· Heating elements in ovens and on ranges

· Heat lamps

· Toaster ovens

· Tea kettles

APPLICATION

Materials

Property of LS&A Physics Department Demonstration Lab

1 green multimeter (with leads)

1 battery board

1 alligator lead card

1 carbon pencil

Property of LS&A Physics Department Demonstration Lab

1. Starting with the Single-Strip Shading Regions on the Ohms Law Resistor Sheet, shade in the 0.2 and 0.6 inch regions with a carbon pencil. Press firmly with the pencil to get a thick layer of carbon on the sheet.

· Measure the resistance of 0.2 inch region.

· Predict the resistance of the 0.6 inch region. That region will have three times as much carbon because it is three times as high as the first region. Will the region have the same, higher, or lower resistance? Discuss with your group and explain your prediction. Measure the resistance.

To measure the resistance of the region set the multimeter to ohms (Ω). Lay one probe along one end of the region horizontally (more surface area means better reading), and the other probe on the other end of the region horizontally.

Region / Predicted Resistance (Ω) / Measured Resistance (Ω) / Explanation of Prediction
0.2 inch / NA / NA
0.6 inch

Does this measurement agree with your predictions? Explain how the height of the shaded region affects resistance.

2. Now use the Parallel Paths Shading Regions section of the Resistor Sheet. Shade in the two large boxes on the left and right.

· Then shade in one of the parallel paths which can be thought of as an individual connecting resistor. First predict what the resistance will be, then measure the resistance by placing the probes in either of the large boxes on the end. Remember where you place the probes and measure from the same place each time for consistency. Record the resistance of 1 path alone below.

· Predict and explain what the resistance of 2 paths will be. Continue to predict and add paths until you’ve filled all 4.

Number of Parallel Paths / Predicted Resistance / Measured Resistance / Explanation of Prediction
1
2
3
4

Explain how parallel paths affect the resistance.

Now shade in the horizontal sections (1, 2, 3, and 4) of the Series Shading Regions of the worksheet, but do not shade in the connecting paths marked with dashed lines.

3. Measure the resistance of each individual region.

Horizontal Region / Resistance (Ω)
1
2
3
4

· Predict the resistance of paths 1 and 2 combined in series. Explain your prediction. Measure and record.

· Predict the resistance of paths 1, 2, and 3 combined in series. Explain your prediction. Measure and record.

· Predict the resistance of paths 1, 2, 3, and 4 combined in series. Explain your prediction. Measure and record.

Remember, the resistance is measured across the longest length of the two regions (e.g. for 2 series paths you should be measuring near where it’s labeled “1” and “2”).

Number of Series Paths / Predicted Resistance (Ω) / Measured Resistance (Ω) / Explanation of Prediction
2
(1 and 2 combined)
3
(1, 2, and 3 combined)
4
(1, 2, 3, and 4 combined)

4. Discuss with your group and explain how series connections contribute to resistance. How does this compare to parallel?

Challenge Work

5. Explain how the mulitmeter measures the resistance when you connect the leads across a resistor.

Summary:

1. A resistor for which the potential required to drive a current is proportional to the current obeys Ohm’s Law: V = I R.

2. The resistance of an “Ohmic” resistor (one that obeys Ohm’s Law) is the constant of proportionality between current and potential: R = V/I.

3. The units of resistance are volts per ampere (V/A) which are denoted as Ohms (Ω) in honor of the physicist Ohm who made early studies of electrical resistance.

4. The graph of potential versus current for a resistor which obeys Ohm’s Law is a straight line and the slope of the line is the resistance of the resistor (change in potential divided by change in current).

5. Ohm’s “Law” is not a law at all, it’s actually a definition. Many devices do not exhibit a simple proportionality between current and voltage. Semiconductor devices such as diodes and transistors are useful precisely because they are nonlinear and do not obey Ohm’s “Law”. If Ohm’s Law were truly a law for solid matter, we would still be using vacuum tubes to build electronics—transistors would not be possible!

6. The equivalent resistance increases as resistors are added in series and is obtained by adding the individual resistances: Req = R1 + R2 + R3 + …

7. The equivalent resistance decreases as resistors are added in parallel and is calculated as: 1/ Req = 1/R1 +1/R2 + 1/R3 + …

8. At low temperatures some materials lose all electrical resistance and become perfect conductors called superconductors. Superconductors can be used to build very powerful electromagnets and to levitate objects magnetically by exploiting the Meissner effect whereby a superconductor expels all magnetic fields from its interior so that a magnet will sit suspended above the surface of the superconductor supported by magnetic forces. If superconductivity can be achieved at room temperature, magnetic levitation of trains will become truly practical as well as loss-free transmission of electrical power over wires. To date the highest temperature superconductors operate near the temperature of liquid nitrogen (77 degrees Kelvin, equivalent to 77 Celsius degrees above absolute zero).

Final Clean-up

Please disconnect all alligator leads and reattach them to the clip card. Discard the Ohms Law resistor sheet you colored in with the pencil. Replace all equipment to the carts.

OHM’S LAW

ANALYSIS

Resistance is a measure of how much a circuit component resists the flow of current. A component with high resistance will not allow as much current to pass for a given voltage as would a low resistance component.

Ohmic Resistors

Resistors like the one you used in Step 2 are “ohmic”, that is, they obey Ohm’s Law:

Ohm’s Law states that voltage across a resistor is equal to the current passing through the resistor multiplied by the resistance of the resistor (V varies linearly with I, and vice versa). This defines resistance as the ratio of current and potential. Ohm’s “Law” is not a law at all— semiconductor electronic components such as diodes and transistors are useful precisely because they do not exhibit a simple linear relationship between current and voltage.

Non-Ohmic Resistors

All resistors, such as the light bulb filament, become non-Ohmic when sufficiently hot. That is, their resistances changes (with temperature) and is not a single well defined number. Your measurements should have shown that the bulb did not draw current in strict proportionality with voltage. In the case of the light bulb, the resistance increases as the light bulb heats up.

Property of LS&A Physics Department Demonstration Lab