Discussion:Ohm's Law describes the relationship between the resistance (R) of a wire, the voltage drop across it (V), and currentthrough it (1):V = RI(1)Applying a known current to a wire and measuring the voltage across it will let you determine the resistance of thewire by solving equation 1:(2)The resistance of a particular element depends on its geometry, the resistivity and the temperature. Resistivity is thetendency of the material to behave as a resistor and is an inherent property of a material, in the same sense that density orthermal expansion are inherent properties. Materials with lower resistivity, like copper, are good conductors of electricityand widely used in cireuit components while those with larger resistivity, like rubber, are used as insulators.For a wire with length (L), cross-sectional area (A), and made from a material with resistivrity (p) the resistance (R)will be given by the following equation:R= ,L(3)In case that the geometry (length and cross sectional area) and the resistance of the wire is known, then is possible tocaleulate the resistivity solving equation 3:RA(4)A wire can be consider as a long cylinder; then the cross sectional area would have a circular shape as shown inFigure 2..Cross SectionalAreaLengthFigure 2Then the cross sectional area of the wire can be caleulated using the equation of the area of a cirele:A = mr?(5)In this experiment, you will measure V and I to determine R for various lengths of wire. You will then make a graphof Resistance (Y-axis) versus length (X-axis). The plot will result in a straight line that has a slope equal toslope =,(6)From equation 6, it is possible to solre the resistivity in terms of the slope and the cross sectional area:p = slope + A(7)The manufacture values of the resistivrity corresponding to the wires used in the experiment are reported in Table 1.These values will be used as the theoretical when caleulating percent error.Table 1. Theoretical resistivity of different materials according to manufacturer.| Attractedto Magnet Dinmeter (m)NoMaterialColorResistivity (Qm)7.0 x10*BrassYellow0.0005080.0008130.0010160.001270CopperNicbromeNoDark Gray NoDark Gray1.8 x10*105 x1079 x10Red0.0010160.001016StainlessYes0.001016Steel Table 3 - Resistivity of Different MaterialsLength of the wires: 0.240 mCross SectionalCalculateTheoreticalDiameterResistanceVoltage(V)СuтеntPercentAreaResistivityResistivity(m)(A)( )( )( )Error0.0010160.005751.097750.0010160.29340.961210.0010160.22000.95525

Table 3 - Resistivity of Different Materials Length of the wires: 0. 240 m Cross Sectional Caleulate Theoretical Diameter Voltage Current Resistance Percent Area Resistivity Resistivity (m) (V) (A) Error ( ) 0.001016 0.00575 1.09775 0.001016 0.2934 0.96121 0.001016 0.2200 0.95525

Table 3 - Resistivity of Different Materials Length of the wires: 0. 240 m Cross Sectional Caleulate Theoretical Diameter Voltage Current Resistance Percent Area Resistivity Resistivity (m) (V) (A) Error ( ) 0.001016 0.00575 1.09775 0.001016 0.2934 0.96121 0.001016 0.2200 0.95525

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Discussion:
Ohm's Law describes the relationship between the resistance (R) of a wire, the voltage drop across it (V), and current
through it (1):
V = RI
(1)
Applying a known current to a wire and measuring the voltage across it will let you determine the resistance of the
wire by solving equation 1:
(2)
The resistance of a particular element depends on its geometry, the resistivity and the temperature. Resistivity is the
tendency of the material to behave as a resistor and is an inherent property of a material, in the same sense that density or
thermal expansion are inherent properties. Materials with lower resistivity, like copper, are good conductors of electricity
and widely used in cireuit components while those with larger resistivity, like rubber, are used as insulators.
For a wire with length (L), cross-sectional area (A), and made from a material with resistivrity (p) the resistance (R)
will be given by the following equation:
R= ,L
(3)
In case that the geometry (length and cross sectional area) and the resistance of the wire is known, then is possible to
caleulate the resistivity solving equation 3:
RA
(4)
A wire can be consider as a long cylinder; then the cross sectional area would have a circular shape as shown in
Figure 2.
.
Cross Sectional
Area
Length
Figure 2
Then the cross sectional area of the wire can be caleulated using the equation of the area of a cirele:
A = mr?
(5)
In this experiment, you will measure V and I to determine R for various lengths of wire. You will then make a graph
of Resistance (Y-axis) versus length (X-axis). The plot will result in a straight line that has a slope equal to
slope =,
(6)
From equation 6, it is possible to solre the resistivity in terms of the slope and the cross sectional area:
p = slope + A
(7)
The manufacture values of the resistivrity corresponding to the wires used in the experiment are reported in Table 1.
These values will be used as the theoretical when caleulating percent error.
Table 1. Theoretical resistivity of different materials according to manufacturer.
| Attracted
to Magnet Dinmeter (m)
No
Material
Color
Resistivity (Qm)
7.0 x10*
Brass
Yellow
0.000508
0.000813
0.001016
0.001270
Copper
Nicbrome
No
Dark Gray No
Dark Gray
1.8 x10*
105 x10
79 x10
Red
0.001016
0.001016
Stainless
Yes
0.001016
Steel

Table 3 - Resistivity of Different Materials
Length of the wires: 0.240 m
Cross Sectional
Calculate
Theoretical
Diameter
Resistance
Voltage
(V)
Сuтеnt
Percent
Area
Resistivity
Resistivity
(m)
(A)
( )
( )
( )
Error
0.001016
0.00575
1.09775
0.001016
0.2934
0.96121
0.001016
0.2200
0.95525

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