What is electrical resistance?
Resistance R is a characteristic of a particular object and depends on the material it is made of; its length and cross-sectional area are also important. Resistivity ρ (Greek letter Rho) characterizes the material in general.
The unit of resistance is the ohm (Ω).
The resistance of a conductor that obeys Ohm's law (R=V/I) is given by:
L: Length of the conductor.
A: Cross-sectional area.
ρ: Resistivity of the conductor material (Greek letter Rho).
Illustration 1.- Resistivity of an electrical conductor.
The quantity R is constant for a given conductor and is called the resistance of the conductor. The higher the resistance of the conductor, the lower the current flowing through it when a certain potential difference (Voltage) is applied.
To conclude.
Ohm's law is not a physical principle but an experimental relationship that most metals obey within a wide range of voltage and current values.
Resistance within electrical circuits
When analyzing these circuits, it is convenient to replace the combination of resistors with a single equivalent resistor Req
The equivalent resistance of a set of resistors depends on how they are connected, as well as their values.
Illustration 2.- Resistor for electronics.
There are two ways to combine resistors: in series and in parallel.
Series resistors
If the resistors are connected in series, i.e., one after another, the equivalent resistance Req of the combination is the sum of the individual resistances.
The total equivalent resistance Req will be the sum of the resistances from point A to point B.
Example:
Calculate the value of Req of the following resistors.
The value of Req will be the result of the sum from R1 to R11, resulting in the following expression:
Parallel resistors
In a set of parallel resistors, the corresponding ends of each resistor are connected to the same point.
The inverse 1/R of the equivalent resistance of the combination is the sum of the inverses of the individual resistances:
The following expression is also commonly used:
Where Req is equal to the inverse of the sum of the inverses of each of the parallel resistors.
Example:
To solve the proposed example, we observe that there are two blocks of resistors connected in parallel. I will first solve these blocks, resulting in the following two expressions.
Now, all that remains is to solve a simple series circuit of resistors by adding the 3 resistors and obtaining an Req.
