Electrical resistance quantifies how strongly a material opposes to the flow of electrons. The resistance of a component is defined by 3 different parameters (see the equation below):

  • The resistivity coefficient

  • The length of the component

  • The cross-sectional area of the component

Formula of resistance. Resistance R is equal to the resistivity coefficient rho times the length l, divided by the cross sectional area a.

Figure 1. Formula of Resistance

Resistivity coefficient

The resistivity coefficient is basically dependant on the material. Some materials conduct electricity more easily than others just because of their internal structure. For example, electrons in metals are not fixed to one atom but instead are shared around all the piece of metal. This makes electrons in metals way easier to move (low resistance to current), and since the electric current is basically moving electrons, it facilitates the current.


Length is a basic parameter in resistors, and the bigger it is, the bigger is the resistance of the resistor. The resistance of a material is based on how likely is that the electrons of the current will impact other electrons on their way through the resistor. The longer the component is, the longer is the way the electrons have to go through and the higher the chances that the electrons will bump into each other, causing resistance to the pass of current.

Cross-sectional area

The cross-sectional area influence in current can be explained by using the same explanation as before. If we consider a resistor that is thicker, it means that the current has more space to go through the resistor than in a thinner resistor. More space to go through the resistor means less chance that the electrons will bump into each other and consequently, less resistance to the current. The bigger the cross-sectional area, the smaller the resistance of the resistor.

Additionally, other variables can modify the resistance of a resistor. One of the most common (especially for its utility) is the temperature. When we increase the temperature of a material, we excite the electrons. When electrons are excited they vibrate faster and with bigger amplitude. The more the electrons vibrate, the higher the chance that the electrons bump into each other, difficulting the pass of current. In the other hand, if we cool down a resistor enough (close to 0 K, -273ºC) the electrons in the material (this only happens in some materials) will stop bouncing completely. When this happens, the resistance to the pass of the current of that material is close to zero. This is called a superconductor.