The electrical resistance is the opposition that a material or component offers to the flow of current.
So far we have seen that a potential difference can produce current. However, not all materials allow charge to pass through with the same ease.
Electrons, on their journey through the conductor, do not have a clear path. They constantly collide with the atoms of the material’s structure. These collisions slow down the flow.
We call this natural opposition Electrical Resistance.
Resistance (R) and Conductance (G)
Resistance (R) is the measure of how much an object opposes the flow of electric current.
- Its unit in the International System is the ohm (represented by the Greek letter
). - 1Ω is defined as the resistance that allows the passage of 1A when 1V is applied.
The Other Side of the Coin: Conductance
Sometimes, in engineering (especially when analyzing parallel circuits), we are interested in the opposite: measuring “how much an object facilitates” the flow of current.
We call this Conductance (G), and it is simply the inverse of resistance.
Its unit is the siemens (S).
Although we will almost always use ohms, it is good to remember that if something has high resistance, it has low conductance, and vice versa.
Resistivity (ρ): A Material Property
This is where many people get confused.
- Resistance (R) is a property of a specific object (e.g., “this 3-meter piece of wire”).
- Resistivity (ρ) is an intrinsic property of the material (e.g., “copper”).
We cannot say “how much resistance does copper have?”. The correct question is “how much resistivity does copper have?”. The resistance will depend on how much copper we use and what shape we give it.
Resistivity (ρ) is measured in Ω / m (or more commonly in engineering
- Copper:
(Very low, conducts excellently). - Glass:
(Extremely high, it is an insulator).
The Geometry of Resistance
We can now calculate the resistance of any wire or object if we know its dimensions and material. The fundamental formula is:
Let’s analyze this formula, as it is pure physical logic:
- ρ (Resistivity): It is the “roughness” of the path. Rougher → More Resistance.
- L (Length): It is how long the path is. The longer the wire, the more collisions the electrons will suffer → More Resistance.
- S (Cross-section or Area): It is the width of the path. The thicker the wire, the more “lanes” electrons have to pass through comfortably → Less Resistance.
Practical example: If you have a very long cable powering a pool pump and you get low voltage at the end, the problem is that the Resistance (R) of the cable is high due to the great Length (L).
The solution? Increase the Cross-section (S) by using a thicker cable. By dividing by a larger number, the total Resistance decreases.
The Effect of Temperature
So far we have assumed that resistance is constant. But in the real world, temperature changes everything.
Remember that temperature, at the atomic level, is vibration. The atoms of the material are not still; they vibrate.
- If we heat a metal, its atoms vibrate more strongly and with greater amplitude.
- For an electron trying to cross, this is like trying to cross a dance floor full of people jumping wildly. It is much more likely to collide.
Therefore, in conductive metals and within their usual range: the higher the temperature, the higher the resistance.
The Temperature Coefficient (
We can calculate how much the resistance changes using this linear approximation:
Where:
- Rf: Final resistance (hot).
- R0: Initial resistance (at room temperature, usually 20ºC).
- α: Temperature coefficient of the material.
- ΔT: Temperature increase.
For copper,
Curiosity: This property is the basis for temperature sensors like the RTD or PT100. We measure the resistance of a platinum wire and, knowing its α, we calculate the exact temperature.
