Quantitative Investigation of Resistivity and Ohm’s Law

Quantitative Investigation of Resistivity and Ohm’s Law

Blessy M. Eroy1, Joshua P. Gemperoso2*, Genevieve R. Ocampo3, Marianne I. Rigor4 and Keith Philip L.

Tidon5

1,3,4 College of Engineering and Agro-Industrial Technology, UP Los Baños

2,5 College of Arts and Sciences, UP Los Baños
*Corresponding Author: joshua_gemperoso@yahoo.com

Abstract

The exercise investigated the difference between resistance and resistivity by measuring the resistance of materials with varying length and cross-sectional areas, and materials of different composition. It exploited Ohm’s law by measuring the current of a circuit with varying, and constant resistance. It was found out that resistance is a quantity dependent on length and cross sectional area, while resistivity depends on material composition. The result also showed that current linearly varies with voltage.

Keywords: resistance, resistivity, Ohm’s law

Introduction

Current, resistivity and resistance are very common terms in electromagnetism. In fact, they are very important in the world today, especially in the light industry. Without these concepts, Thomas Edison would not have invented the light bulb and people would not have experienced using the switch. Thus, it is also important for us to know these concepts. Uniting all these terms is Ohm’s law.

Ohm’s law takes on many different forms. The most useful forms used in this exercise is the relationship seen below:

        [pic 1]

where  is the current density,  is the electric field,  is the resistivity, V is the voltage, I is the current and R is the resistance. In order to understand Ohm’s law better, definition of the terms should be known.[pic 2][pic 3][pic 4]

Current, in simplest terms, is the rate of charge flow inside a material [1]. It is also described to be the flow of charge from one cross sectional area to another as seen in figure 1 [2]. It is described by the equation:

[pic 5]

where n is the number of charged particles, q is the charge,  is the drift speed, and A is the cross sectional area of the object. It can be seen through this definition that current on the cross sectional area of an object. For a current’s sign, when a positive charge moves along a positive direction and a negative charge moves along a negative direction, it is positive. On the other hand, when either a positive charge moves along a negative direction and vice versa, the current obtains a negative charge [1]. [pic 6]

[pic 7]

Figure 1. Motion of charges from one cross sectional area to another [2].

Bridging current and resistivity is the concept of current density. Current density is the current per cross sectional area which is described by equation 3. It is a vector quantity which has the same direction as the electric field. As described by Ohm’s law, resistivity is equal to the electric field divided by the current density.

[pic 8]

Resistivity is the ratio of the electric field and current density given by the equation:

[pic 9]

This ratio consequently means that the greater the resistivity a material, the greater the electric field it has and the smaller its current flow per point in an area [2]. A perfect conductor has zero resistivity, which ultimately means that charges are perfectly free to move around the material [2].

To give a glimpse of how resistance is different from resistivity, let us first define resistance. It is the ratio of potential difference (V) to current (I).

[pic 10]

Since charge has a natural tendency to move from higher potential to lower potential, the potential difference is the potential drop of the given material from point to point in a cross sectional area as seen in figure 2. Because of this, resistivity and resistance are two different quantities.

[pic 11]

Figure 2. Natural tendency of charge to move from higher potential to lower potential [2].

With these definitions in mind, this exercise aimed to differentiate resistivity and resistance, determine various factors affecting resistance and resistivity, measure the resistance and resistivity of different wires, determine the relationship between current passing through the resistor and the voltage across it and lastly, measure the current passing through a resistor with different values at a constant voltage.

Methodology

Figure 2 represents the configuration of apparatuses used in this exercise.

[pic 12]

Figure 2. Exercise 3 circuit set – up

For the first part of the experiment (resistance and resistivity), the ohmmeter was used to measure the resistance of each wire and the observations were recorded. Comparisons between resistance of different materials when length and cross sectional area were changed were made. After that, computations for the resistivity of the materials (Cu and Cu-Ni) were done.

For the second part of the experiment (variation of voltage with current with resistance being constant), the set – up described in figure 2.1 was utilized. The value of the resistance was fixed to a value of 10 Ω. The ohmmeter was the used to measure the actual resistance of the resistance box. Voltage was then varied by 1.0V and the ammeter readings were recorded. Expected values for the current in each voltage reading was also computed for further comparison between experimental values and a graph was constructed to see the graphical relationship of current and voltage.

For the last part of the exercise (variation of current with resistance with voltage being constant), the same set – up (see figure 2.1) was used. The voltage was fixed to 3V. Variation of resistance using the resistance box was done and the current readings were recorded based on each resistance value. Also, expected values for the current were generated to enable comparison between experimental values obtained. Graphical analysis was also done by constructing the graph of resistance versus current, then used linear regression to calculate the slope of the graph, its y-intercept, and its linearity.

Results and Discussion

The first part of the exercise dealt with the measurement of resistance and resistivity of different materials of different lengths and cross-sectional areas, and of different material composition. The resistance R of any material to electrical current flow is a function of its composition, length, cross-sectional area and temperature. Since the experiment is assumed to be at constant temperature, the resistance R is given by:

[pic 13]

where L is the length measured in meters (m), A is the cross-sectional area measured in square meters (m2) and ρ is the resistivity, a constant dependent on composition measured in ohm-meters (Ω-m). Resistivity ρ is also a function of temperature. A perfect conductor would have zero resistivity, and a perfect insulator would have an infinite resistivity. Metals and alloys have the smallest resistivity and are the best conductors. Resistance usually increases with temperature, but semiconductors, the opposite is true [2].