material depend on its conductivity
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Answer:
Resistivity of materials is the resistance to the flow of an electric current with some materials resisting the current flow more than others
Ohms Law states that when a voltage (V) source is applied between two points in a circuit, an electrical current (I) will flow between them encouraged by the presence of the potential difference between these two points. The amount of electrical current which flows is restricted by the amount of resistance (R) present. In other words, the voltage encourages the current to flow (the movement of charge), but it is resistance that discourages it.
We always measure electrical resistance in Ohms, where Ohms is denoted by the Greek letter Omega, Ω. So for example: 50Ω, 10kΩ or 4.7MΩ, etc. Conductors (e.g. wires and cables) generally have very low values of resistance (less than 0.1Ω) and thus we can neglect them as we assume in circuit analysis calculations that wires have zero resistance. Insulators (e.g. plastic or air) on the other hand generally have very high values of resistance (greater than 50MΩ), therefore we can ignore them also for circuit analysis as their value is too high.
But the electrical resistance between two points can depend on many factors such as the conductors length, its cross-sectional area, the temperature, as well as the actual material from which it is made. For example, let’s assume we have a piece of wire (a conductor) that has a length L, a cross-sectional area A and a resistance R as shown.
A Single Conductor
resistivity of a single conductor
The electrical resistance, R of this simple conductor is a function of its length, L and the conductors area, A. Ohms law tells us that for a given resistance R, the current flowing through the conductor is proportional to the applied voltage as I = V/R. Now suppose we connect two identical conductors together in a series combination as shown.
Doubling the Length of a Conductor
doubling the length of a conductor
Here by connecting the two conductors together in a series combination, that is end to end, we have effectively doubled the total length of the conductor (2L), while the cross-sectional area, A remains exactly the same as before. But as well as doubling the length, we have also doubled the total resistance of the conductor, giving 2R as: 1R + 1R = 2R.
Therefore we can see that the resistance of the conductor is proportional to its length, that is: R ∝ L. In other words, we would expect the electrical resistance of a conductor (or wire) to be proportionally greater the longer it is.
Note also that by doubling the length and therefore the resistance of the conductor (2R), to force the same current, i to flow through the conductor as before, we need to double (increase) the applied voltage as now I = (2V)/(2R). Next suppose we connect the two identical conductors together in parallel combination as shown.
Doubling the Area of a Conductor
doubling the area of a conductor
Here by connecting the two conductors together in a parallel combination, we have effectively doubled the total area giving 2A, while the conductors length, L remains the same as the original single conductor. But as well as doubling the area, by connecting the two conductors together in parallel we have effectively halved the total resistance of the conductor, giving 1/2R as now each half of the current flows through each conductor branch.
Thus the resistance of the conductor is inversely proportional to its area, that is: R 1/∝ A, or R ∝ 1/A. In other words, we would expect the electrical resistance of a conductor (or wire) to be proportionally less the greater is its cross-sectional area.
Also by doubling the area and therefore halving the total resistance of the conductor branch (1/2R), for the same current, i to flow through the parallel conductor branch as before we only need half (decrease) the applied voltage as now I = (1/2V)/(1/2R).
So hopefully we can see that the resistance of a conductor is directly proportional to the length (L) of the conductor, that is: R ∝ L, and inversely proportional to its area (A), R ∝ 1/A. Thus we can correctly say that resistance is:
Proportionality of Resistance
proportionality of resistance
But as well as length and conductor area, we would also expect the electrical resistance of the conductor to depend upon the actual material from which it is made, because different conductive materials, copper, silver, aluminium, etc all have different physical and electrical properties. Thus we can convert the proportionality sign (∝) of the above equation into an equals sign simply by adding a “proportional constant” into the above equation giving: