The resistance of a resistor is modeled by the equation
(1)
Where R is the resistance (Ω), L is the length (m), A is the cross-sectional area (m2), and ρ is a constant dependent upon the material called the resistivity (Ω-m). The length, thickness, and material of a wire affect its resistance of the wire. Some materials have lower resistances than others. For example, the resistivity of Copper is 1.72×10-8 m (Ω-m) and is one of the lowest resistivities only second to silver. Nickel on the other hand has a resistivity of 7.8×10-8 m. The longer and narrower the wire, the higher the resistance. It’s harder for the electrons to move in a longer, narrow hallway. Figure 1 gives a visual of a segment of wire and the quantities that are measured for resistance. In this lab, the values of length and resistivity are given.
Figure 1: A uniform cylinder of length l and cross sectional area A. The longer the cylinder, the greater its resistance. The larger its cross-sectional area A, the smaller its resistance. Image credit: Adapted from OpenStax College Physics. Original image from OpenStax, CC BY 4.0
Use the following link to complete the lab activity.
https://phet.colorado.edu/sims/html/resistance-in-a-wire/latest/resistance-in-a-wire_en.html
Part 1 – Vary the length keeping the cross-sectional area fixed
⦁ Keeping the cross-sectional fixed at 7.50 cm2 and resistivity at 0.50 , vary the length 10 times, and tabulate length and resistance.
Length, L (cm) Resistance, R (
⦁ Plot R vs L on excel. Make sure to display the equation of the fit line and R2 value. Copy and paste it here.
⦁ Equate the slope of the line to , and then calculate
⦁ Compare the found experimental with the known value of to find %error.
Part 2 – Vary the cross-sectional area keeping the length fixed
⦁ Keeping the length fixed at 10 cm and resistivity at 0.50 , vary the cross-sectional area 10 times , and tabulate area, inverse area and resistance.
Area, A (cm2) Inverse Area, A-1 (cm-2) Resistance, R (
⦁ Plot R vs A-1 (i.e. R along y-axis and A-1 along x-axis) on excel. Make sure to display the equation of the fit line and R2 value. Copy and paste it here.
⦁ Equate the slope of the line to , and then calculate
⦁ Compare the found experimental with the known value of to find %error.
Part 3 – Conclusions
⦁ What is the relationship between the length and the resistance of the resistor? Discuss in the context of your plot. If the length of the given resistor is twice as much, what would be the corresponding resistance?
⦁ What is the relationship between the cross-sectional area and the resistance of the resistor? Discuss in the context of your plot. If the radius of the given cylindrical resistor is twice as much, what would be the corresponding resistance?
⦁ A copper wire has a diameter of 0.5 mm and resistivity of 1.6 x 10-8 Ωm. What will be the length of this wire to make its resistance 10Ω? How much does the resistance change if the diameter is doubled?
