Resistors in Series and Parallel

It is not uncommon to occupy a resistance with a high value in a circuit. Sometimes a resistance with a value so high or so irregular is occupied that it would become very expensive to start a factory to make it. Fortunately, there is the possibility of joining several small resistances to form a large one, or putting together different resistance values to make an irregular value.

The way in which we put these components together produces resistances in series and in parallel.

Let's see the following configuration:

Resistors in Series 

resistors in series

What happens if we want to go from the positive terminal of the battery to the negative? We must go through all resistances, it is the only way to arrive. This is what is called a series circuit, it is a circuit where the resistances are linked in such a way that there is only one route to go from one end of the circuit to the other.

Let's say now that we have the following:

Resistors in Parallel

Resistors in Parallel

Resistors in Series and Parallel

What happens if we want to get from one battery terminal to the other? There are three routes to do it, we can go through the first resistance or through the second, or the third as indicated in the following figure:

parallel of resistances

 This is what is known as a parallel of resistances. It is a circuit where there are multiple routes to get from one place to another. We do not even have to go through a single resistance, we can also pass part of the current through the first resistance and another part through the rest (this is what happens in a real circuit).

Generally when we are doing electronic diagrams we do not draw the resistances as they are in real life. In diagrams, the resistance is represented as a broken line with two extensions. Also some software tools to draw circuits represent it as a rectangle:

draw circuits resistance

In circuit diagrams, resistance is also sometimes named, in order to identify it more easily. That is what the R1 and R2 means (resistance # 1, resistance # 2). And in some cases the value is set below, although this is not so common because the diagrams become very difficult to read.

In the diagrams we can represent parallels and series. A parallel of resistances is drawn like this:

Resistance in parallel

Equivalent resistance of a series

When we put together several resistors either in series or in parallel, the effect it gives us is as if we had a bigger resistance. All the resistors work together, and each one takes a part of the circuit current. The resistance that is formed together is what is called the equivalent resistance, or Req.In a series circuit, the equivalent resistance is easy, just add the values of the series resistance

Equivalent resistance of a parallel

In the case of a parallel resistance, there are two possibilities to solve it. The first equation is the following:

This equation has the disadvantage that it only works with two resistors at the same time. To solve a parallel of three resistances, we must first obtain the equivalent resistance of two of them and then that equivalent resistance make it in parallel with the third.


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