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Online Lab: Resistivity
Name: Date:
Instructor: Section:
Objective:
The resistivity of different metals is determined by finding the resistance of wires of a known diameter as a function of their length. It is also shown that the resistance of a wire of fixed length is inversely proportional to its cross-sectional area.
Theory:
Resistivity (ρ) is a fundamental material property, while the resistance (R) of an electrical con- ducting wire depends on several factors, such as: type of conductor material, length of the conductor, cross-sectional area, and the temperature of the wire. At a constant temperature, the resistance (R) of a given conductor is directly proportional to its length (L) and inversely proportional to its cross-sectional area (A).
This resistance is given by the following formula:
R = ρL/A (1)
A plot of R vs. L will result in a straight line that has a slope equal to ρ/A. Thus the resistivity is given by
ρ = (slope) A = (slope) π r^2 = (slope) π (d/2)^2 (2)
Online Experiment Setup Instructions
- Today’s Online Lab we are going to use one of the physicsaviary.com simulations. Go to the following website: http://www.thephysicsaviary.com/Physics/Programs/Labs/ResistanceOfWireLab/
- The figure below shows what you should see on your screen. Click Begin to start the simulation.
’ Click the Wire to change the Length, L
Click here to change Wire Type
Copper, Aluminum, Nichrome, Silver, Graphite, Gold
Resistance, R
How to Measure the Wire Cross-Section
Measure the radius of the wire by counting the number of blocks in the grid. For example, in the Wire Cross Section on the right, the cross section is about 6.0 blocks from the center of the wire to the edge for a wire radius: r = 0.1 mm × 6.0 = 0.6 mm = 0.0006 m.
r
The Cross-Sectional Area, A of a wire can be found by: A = π r^2. In the example to the right,
A = π r^2 = π × (0.0006 m)^2 A = 1.13 × 10 −^6 m^2 or 1.13 E -6 m^2
Data Section: Resistance vs Length
Table 2: Resistance versus Length
Wire Length (m)
Copper Resistance (Ω)
Aluminum Resistance (Ω)
Nichrome Resistance (Ω)
Silver Resistance (Ω)
Table 3: Resistivity of Different Metals for Wire Length between 7 and 8 meters
Metal Slope (Ω/m)
ρexperimental (Ω m)
ρaccepted (Ω m)
%error
Copper 1.68 × 10 −^8 Aluminum 2.65 × 10 −^8 Nichrome 100 × 10 −^8 Silver 1.59 × 10 −^8
Data Analysis: Resistance versus Length
- Using your data in Table 2, create a scatter graph of Resistance, R on the Y-axis versus Length L on the X-axis for each of the 4 types of wires. Label the x-y axes including units and Title your graph with Metal Resistance vs Length. See Figure 1 for an example graph. For example, “Copper Resistance vs Length“. Comment on your graphs below. Upload your graphs with this Lab Report in D2L.
- Measure the slope of the line for each of the 4 graphs using any method you are comfortable with. Record the slope values in Column 3 of Table 3.
- Use Equation 3 to calculate the measured resistivity, ρexperimental using your slope values and the measured Cross sectional Area in Table 1 for each of the metals in Table 3. Record these values in Column 4 of Table 3.
- Compare your measured resistivity values ρexperimental to the accepted resistivity values ρaccepted using the equation below. Record these values in Column 6 of Table 3. Do they agree? Explain any differences.
%Error =
ρexperimental − ρaccepted ρaccepted
× 100 (3)
- Take a photo or scan a copy showing ALL of your calculations and upload it with this Lab Report in D2L.
Data Analysis: Resistance versus Cross-Sectional Area
- Using your results from Table 4, create a scatter graph of Resistance (Ω) on the Y-axis versus 1/A (× 106 m−^2 ) on the X-axis. Label the x-y axes including units and Title your graph: Resistance vs Cross Sectional Area. See Figure 2 for an example graph. Calculate the slope of the line. What is the physical meaning of the slope? Upload your graph with this Lab Report in D2L.
- From the slope of the line, find the resistivity of gold:
Resistivity of gold, ρexperimental = SLOP E L^ ×^10 −^6 =
- Compare your measured resistivity value for gold ρexperimental to the accepted value of ρaccepted = 2.44 × 10 −^8 (Ω m). Do they agree? Explain any differences.
%Error =
ρexperimental − ρaccepted ρaccepted
× 100 (4)
- Take a photo or scan a copy showing ALL of your calculations and upload it with this Lab Report in D2L.
Figure 1: Example graph of Resistance versus Length.
Figure 2: Example graph of Resistance versus Cross Sectional Area.
