Experiment on Investigation of Resistivity

Topic:

Resistivity experiment

Experiment on Investigation of Resistivity

Introduction

The resistance of a body is a factor that is dependent on the shape of the material and the components. The resistance of a material is the ratio of voltage and current, as outlined by Ohm’s law (Serway, Vuille & Hughes,2018). The factors that affect resistance include temperature, length, cross-sectional area, and the property of a material. The resistance of material changes with temperature, and therefore, the degree of change varies between pure and non-pure metals (Etkina, Gentile & Heuvelen, 2014). Resistance for a uniform conductor is directly proportional to its length; therefore, the resistance increases with an increase in length (Serway & Vuille, 2007). On the other hand, the resistance is inversely proportional to the cross-sectional area of a material while the property of a material determines the resistance, resistivity is used to define how a material conduct electricity

ThereforeR=ρ L/A (1)

Where R is the resistance, L is the length of the material, while A is the cross-sectional area.

Resistivity is the intrinsic property of a material and dependent on the size and shape (Knight, Jones & Field, 2014). The resistivity of a material is directly proportional to the area and resistance of a material and inversely proportional to the length.

ρ=AR/L (2)

Resistivity determines the ability of the material to conduct electricity. The materials can be classified as conductors, semiconductors, and insulators, depending on the property of resistivity. The unique properties of the materials make them applicable for different functions. Therefore resistivity is important in distinguishing the different types of materials.

Questions

a) The resistance increases with the increase in resistivity ρ because the resistance is directly proportional to the length and inversely proportional to the resistance. Resistivity is a constant value that increases the length of a material, thereby increasing resistance.

b) A decrease in the resistivity (ρ) results in the corresponding decrease in the resistance. The property of the material is decreased and therefore leading to a decrease in resistance.

2. a) The increase in length L of the wire increases its resistance. The resistance of a material is directly proportional to the length. An increase in length increases the distance of travel by the electrons.

b) A decrease in length L decreases the resistance of the material. The decrease in length shortens the distance of travel by the particles and therefore decreases in opposition to the flow of current.

3. a) Increase in the area A of the wire decreases the resistance of a material; the increase in the area increases the number of particles per cross-section to conduct electricity.

b) A decrease in area A of the wire increases the resistance of the wire; the decrease in the area reduces the number of particles per cross-section, resulting in high opposition to the current.

4. Resistor I

Resistivity ρ =1.00

Length L =1.01 cm

Area A = 1.01 cm

R=ρL/A=(1×1.01)/1.01=1.00 Ω

Resistor II

Resistivity ρ =0.64

Length L =1.62 cm

Area A= 1.01 cm

=ρL/A=(0.64×1.62)/1.01=1.02 Ω

Resistor III

Resistivity ρ =0.64

Length L =15.65 cm

Area A= 9.89 cm

ρL/A=(0.64×15.65)/9.89=1.01 Ω

5. Cable with resistance III would charge the phone fastest because it has a high cross-sectional area and a suitable length while maintaining the same resistance

Resistance Worksheet

Figure 1A resistor with a resistance of 1Ω

A= 5.89cm2

ρ= 0.49 Ωcm

L= 12.04

R=ρL/A=(12.04×0.49)/5.89=1.00 Ω

The black dots represent the property of a material to conduct electricity or the particles.

Table 1 Relationship between length and Resistance

Method

Resistance Resistivity Area Length

0.1 0.01 0.01 0.10

4.58 0.01 0.01 4.58

8.84 0.01 0.01 8.84

14.1 0.01 0.01 14.13

20.0 0.01 0.01 20.0

Figure 2 Resistance against Length

The graph above shows the variation of the resistance and the resistance of the material. The relationship suggests that an increase in the length of a material increases the resistance. Therefore, the length of the material is directly proportional to the resistance.

R=ρL/A Therefore L=AR/L.

The gradient of the graph gives the area from the equation of y=mx+C

Taking points from the graph as (5, 5) and (19, 19)

Gradient=(19-5)/(19-5)=1

Table 2 A graph of Variation of Resistivity and Resistance

Method

Resistance Resistivity Area Length

0.013 0.01 7.50 10.00

0.360 0.27 7.50 10.00

0.627 0.47 7.50 10.00

0.893 0.67 7.50 10.00

1.23 0.92 7.50 10.00

Figure 3 A graph of Resistance against Resistivity

Taking the arbitrary points as (0.2, 0.28) and (0.8, 1.08)

Gradient =(1.08-0.28)/(0.8-0.2)=0.8/0.6=1.333

The relationship indicates that increase in resistivity increases the resistance. Therefore resistance is directly proportional to the resistivity.

Table 3 Resistance versus area

Method

Resistance Resistivity Area Length

0.001 0.01 0.93 0.10

0.0003 0.01 3.61 0.10

0.0002 0.01 6.06 0.10

0.0001 0.01 9.28 0.10

0.0001 0.01 13.19 0.10

Figure 4 A Graph of area vs resistance

The increase in the area decreases the resistance of the material. The area is inversely proportional to the resistance. Material with the bigger cross-sectional area can easily pass current because of less resistance as compared with material with a smaller cross-sectional area.

Yes, it is possible to decrease the resistance of the wire without changing the material. The decrease in resistance can be done by decreasing the length and increasing the area of the cross-section. Resistance is directly proportional to the length and inversely proportional to the area.

Discussion

The experiment involves the determination of the resistivity of a material by the variation of length and area. The resistivity of a material is dependent on the length and the cross-sectional area. Three quantities were varied in the simulation process, which included length, resistivity, and area. The variable responded differently to the resistance of a material. The resistance decreased with an increase in the area while it increases with an increase in both the length and resistivity. The resistivity of a material determines its property to conduct electricity, and it is dependent on both the length and area of a material (Yoon, Kim, Kim & Lee, 2009). The gradient of the graph of resistance against the ratio of area and length gives the resistivity of a material.

Conclusion

The resistance of a material is directly proportional to the length and inversely proportional to the area. The resistivity of a material is the gradient obtained by the relationship between resistance length and area. The resistivity is also dependent on the size and shape of a material. The experiment can be improved by using different materials to get the best outcome of how different relationships are connected.

References

Serway, R. A., Vuille, C., & Hughes, J. (2018). College physics. Boston, MA: Cengage Learning.

Serway, R. A., & Vuille, C. (2007). Essentials of college physics. Belmont, CA: Thomson-Brooks/Cole.

Knight, R. D., Jones, B., & Field, S. (2014). College physics, third edition: a strategic approach. Boston: Addison-Wesley.

Etkina, E., Gentile, M. J., & Heuvelen, A. V. (2014). College physics. Boston: Pearson Education.

Yoon, H. K., Kim, J. H., Kim, R., & Lee, J. S. (2009, January). Electrical resistivity and cone tip resistance monitoring by using cone resistivity penetrometer. In The Nineteenth International Offshore and Polar Engineering Conference. International Society of Offshore and Polar Engineers.