After having seen the different types of circuits that we can find, today we are going to study the electrical resistance, as well as the steps we have to follow to calculate it depending on the circuit in which we are working.

**DEFINITION**

Electrical resistance is the greater or lesser opposition by electrons to displacement through a conductor. The unit of measurement in the international system for measuring electrical resistance is the ohm (Ω).

To calculate the resistance we use the following formula: Where ρ is the coefficient of proportionality, that is, the resistance of the material, l is the length of the conductor and S is the section of the surface. In addition to this formula, according to the data available to us, we can also use the formula derived from Ohm’s law, which tells us that the intensity of the current flowing between two points in a circuit is proportional to the electrical voltage. From where the following formula is obtained:

Where V is the potential difference measured in volts (V) and I is the current measured in amps (A).

**TOTAL RESISTANCE IN A SERIES CIRCUIT**

When we work with circuits in which the resistors are placed in series, the total resistance of the circuit is obtained by adding the resistors that make up the circuit: Rt = R1 + R2 + … + Rn.

In series circuits the total intensity that the circuit travels is the same as the intensity that passes through each of the points of the circuit.

On the other hand, the total potential difference can be obtained with the Ohm’s law formula from the total resistance. However, if there are voltage drops at each of the points, it can also be obtained by adding: Vt = V1 + … + Vn.

*Ejemplo:** A partir de un circuito formado por tres resistencias en paralelo: R1=3 Ω , R2= 2 Ω y R3=5 Ω y una diferencia de potencial (o voltaje) 120 V, calcula la resistencia total, la intensidad que circula por el circuito y las caídas de tensión en cada resistencia.*

En primer lugar, vamos a calcular la resistencia total: Rt=3+2+5=10Ω .

Una vez calculada la resistencia total, como la intensidad del circuito es la misma en todos los puntos: I=V/R=120/10=12A.

Por último, calculamos las caídas de tensión:

V1=I∙R1=12∙3=36V

V2=I∙R2=12∙2=24V

V3=I∙R3=12∙5=60V.

**TOTAL RESISTANCE IN A PARALLEL CIRCUIT**

The total resistance of a parallel circuit is calculated by making the inverse of the sum of the inverse resistances, that is, using the following formula: Also in a parallel circuit the potential difference is constant as along all the points of the circuit. While the total intensity is calculated using Ohm’s law, as well as that of each branch, which in this case if they are different.

*Example:** From the circuit in the following image, which we know has a potential difference of 100V, calculate the total resistance, the potential difference of the circuit and the intensity at each point: The total resistance is: The difference of The potential of the circuit at each point is the same: V = 100V. The total intensity: I = V / R = 100 / 9.23 = 10.8A While the intensity at each point is: I1 = V / R1 = 100/20 = 5A I2 = V / R2 = 100/30 = 3 , 33A I3 = V / R2 = 100/40 = 2.5A*