How Is Resistivity Calculated and Why Does It Matter?
Resistance to essentials is as important as making the materials to be used in the right places in the electrical and electronic components.
Items used as conductors, for example in a standard electrical outlet need to be able to have a low resistance level. This means that in a given cross-sectional area, the resistance of the fence will be lesser. Choosing the right material depends on knowing its properties, one of which is its resistivity.
For example, copper is a good conductor as it offers a low level of resistance, its cost is not very high, and it also provides other physical features that are useful in many electrical and electronic functions.
Copper is often the most preferred material. Material like copper and aluminum imparts low resistance levels which makes them suitable for the use of power cords and cables. Silver and gold have very low resistivity, but as they are very expensive, they are not widely used. However, silver is sometimes used to refine wires where its low resistance is important, and gold light is used in the joints of many electronic connectors to ensure advanced contacts. Gold is also good for electrical connectors as it does not contaminate or emit oxygen like other metals.
What is Resistivity?
Resistivity is the measure of how much an electrical conductor opposes the flow of current through it.
Resistance has an application in protecting the circuit from high current flow.
When a potential difference (acceleration) is applied across the conductor (to car), the electrons start moving from the negative to the positive electrode).
The current flow increases, the resistance acts as a speed breaker to the accelerated car (high current flow).
The magnitude of the resistance is called resistivity.
Hence it is the magnitude of the resistance of a given size of a specific material or a conductor to electrical conduction.
Resistivity Formula
The resistivity of a material is defined in terms of the measurement of the electric field (E) across it that generates current density (J).
The formula for resistivity is given by,
Where ρ is the proportionality constant known as the resistivity of the material which is the characteristic property of each material.
A = Area of cross-section
L = Length of the material of a conductor
Derive Resistivity
The resistivity of a material depends upon the following factors:
Length
Consider two conductors each of length ‘L’ and the area of cross-section ‘A’
Let V be the same potential difference applied across the ends of two slabs.
The current ‘I’ flowing across each slab will be I/2.
Then resistance via each slab is,
R = V/I (Ohm’s law)
Rs = V/ I/2 = 2 R
So, R increases with the increase in length
R α L …(1)
Area of Cross-section
Each slab of length ‘L’ has a cross-sectional area of A/2.
Similarly, on halving the area of the conductor, the resistance through each of the half slabs will be
R’ = V/ I/2 = 2 R
R increases with the decrease in the area of each half slab.
R α 1/A…(2)
Combining (1) and (2) we get
R α L/A
Removing the proportionality sign we get
Here, ρ is called the electrical resistivity or specific resistance of the material.
Resistivity Definition
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The formula for the resistivity is given by,
R = ρ L/A…(a)
If L =1, A =1, then R = ρ
Thus, the electrical resistivity of a material of a conductor is defined as the resistance offered by the unit length and unit cross-sectional area of a wire of the given material.
Unit of Resistivity
The unit of resistivity is derived from eq(a)
If R = ρ L/A
Then ρ = R.A/L ….(b)
Given unit of R = Ohm (\[(\Omega)\]), A = m2 and L = m
Putting in eq(b) we get
Define Resistivity of a Material
The resistivity is an attribute of each material that is useful in comparing various materials on the basis of their ability to conduct electric currents.
Let’s Discuss the Resistivity of Some Materials is Discussed Below:
Relation Between Conductivity and Resistivity
The relation between conductivity and resistivity can be understood through an example.
You water a lot to the plants during the summer seasons.
If you just sprinkle a few drops of water and won’t supply enough water, after some time, they will get dried and hence die.
Therefore, the more is the resistance to a sufficient supply of water to the plants, the lesser will be their growth (conductivity).
Therefore, high resistivity signifies poor conductors.
Resistivity is symbolized by the Greek letter ‘ρ’ pronounced as ‘rho’ and the conductivity as σ.
So, σ = 1/ ρ or ρ = 1/ σ
Since conductivity is the inverse of resistivity.
Therefore, its unit is mho .m-1\[\Omega\] m-1
Another Unit: Siemens per meter S m17
On What Does Resistivity Depend?
The amount of resistivity also depends on the temperature of the asset; opposing material tables usually set values at 20 ° C. Resistance to steel conductors usually increases with increasing temperature; but resistance to semiconductors, such as carbon and silicon, usually decreases with increasing temperature.
Conductivity is a reciprocal of resistivity, and, again, reflects things on the basis of how well electricity flows through them. The second-kilometer unit of conductivity is mho meter or ampere per volt-meter. There is high conductivity and low resistance in good electrical conductors. Fine insulators, or dielectrics, have high resistivity and low conductivity. Semiconductors have values between both.
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FAQs on Resistivity of Materials Explained for Students
1. What is electrical resistivity and how is it defined?
Electrical resistivity, denoted by the Greek letter rho (ρ), is an intrinsic property of a material that quantifies how strongly it opposes the flow of electric current. It is defined as the electrical resistance (R) of a conductor of that specific material having a unit cross-sectional area (A) and unit length (L). The formula to calculate it is ρ = (R × A) / L. A material with low resistivity is a good electrical conductor, while one with high resistivity is an insulator.
2. What is the fundamental difference between resistance and resistivity?
The key difference between resistance and resistivity lies in what they describe:
- Resistivity is an intrinsic property of the material itself. It is a constant value for a specific material (like copper or silicon) at a given temperature.
- Resistance is an extrinsic property of a particular object or component. It depends not only on the material's resistivity but also on the object's physical dimensions, such as its length and cross-sectional area.
3. What are the SI unit and dimensional formula for resistivity?
The SI unit for electrical resistivity is the ohm-meter (Ω·m). This unit is derived directly from the resistivity formula, ρ = RA/L. The dimensional formula for resistivity, which expresses it in terms of fundamental physical quantities, is [ML³T⁻³A⁻²].
4. How does a change in temperature affect the resistivity of conductors and semiconductors?
Temperature has opposite effects on the resistivity of conductors and semiconductors:
- Conductors (Metals): For conductors, resistivity increases as temperature rises. The increased thermal energy causes the metal's ions to vibrate more, leading to more frequent collisions with the charge-carrying electrons and thus impeding their flow.
- Semiconductors: For semiconductors, resistivity decreases significantly as temperature rises. The additional thermal energy excites more electrons from the valence band to the conduction band, increasing the number of free charge carriers available to conduct current.
5. What is the typical order of resistivity for conductors, semiconductors, and insulators?
Materials are classified based on their vastly different resistivity values:
- Conductors: Have very low resistivity, typically in the range of 10⁻⁸ Ω·m to 10⁻⁶ Ω·m. Examples include silver and copper.
- Semiconductors: Possess intermediate resistivity, generally between 10⁻⁵ Ω·m and 10⁶ Ω·m. Silicon and germanium are common examples.
- Insulators: Exhibit extremely high resistivity, often greater than 10¹⁰ Ω·m. Examples include glass, rubber, and quartz.
6. Why are alloys like nichrome and manganin used for making heating elements and standard resistors?
Alloys such as nichrome and manganin are chosen for these specific applications due to two important properties:
- They have a very high resistivity compared to pure metals. This allows them to generate significant heat (Joule heating) with a moderate current, making them ideal for heating elements in devices like electric heaters and toasters.
- They possess a very low temperature coefficient of resistance. This means their resistance remains relatively stable and does not change significantly with temperature fluctuations, a crucial feature for creating reliable and precise standard resistors for measurement instruments.
7. What is electrical conductivity and how does it relate to resistivity?
Electrical conductivity, represented by the Greek letter sigma (σ), is the measure of a material's ability to conduct electricity. It is simply the mathematical reciprocal of resistivity. The relationship is expressed by the formula σ = 1/ρ. Therefore, a material with high resistivity will have low conductivity, and vice-versa. The SI unit for conductivity is Siemens per meter (S/m).
8. If resistivity is an intrinsic property, how can the conductivity of a semiconductor be altered so dramatically?
While the resistivity of a pure semiconductor is intrinsic, its value is drastically changed through a process called doping. Doping involves intentionally introducing a small, controlled number of impurity atoms into the semiconductor's crystal lattice. These impurities create a large number of extra charge carriers (either free electrons or holes). This massive increase in the density of charge carriers significantly lowers the material's resistivity and, in turn, boosts its conductivity, without changing the fundamental material itself. This principle is the basis of modern electronics.
