The ENEM coming up and several public tenders in the electrical area as well, with that arising several doubts in electrical calculations. In this article, we will show tricks and how to solve the issue of mixed resistor association.
What is a Resistor?
The resistor is a passive electrical component that has the primary function of limiting the flow of electrical current in a circuit. The resistor has a higher resistance than the cables and tracks of an electrical circuit, forcing the reduction of the electric current that passes through the resistor so, the resistor causes a voltage drop.
The relationship between electrical voltage, electrical current and electrical resistance is described by Ohm’s Law. George Ohm was a German scientist who in 1827 discovered that electrical resistance is equal to the voltage divided by the current and this formula is one of the most important when it comes to electrical calculations.
What is Resistance?
The electrical resistance is basically the opposition that a given material offers the passage of the electric current, because the electric resistance generates an “obstacle”, which makes the electric current have a difficulty in traveling through a certain conductor when it is subjected to a certain electric voltage . The unit of measurement used for resistance is ohm (Ω).
Resistor association types
Resistor association is an electrical circuit with two or more resistors. Electrical circuit is one or more closed paths through which the electric current travels, the beginning and the end being at the same point.
There are three types of resistor association, which is the series association, in parallel and mixed. The series association of resistors is a sequence in the connection of the resistors, where the electric current that passes through the resistors is the same. To calculate the equivalent resistance of a series resistor association, we must add the resistances of each resistor.
In the association of resistors in parallel, the resistors are connected at two points in common, thus receiving the same electrical voltage, however the electric current is divided proportionally according to the values of the resistors. To calculate the equivalent resistance of the parallel association of resistors, we must make the product of the resistors over their sum, that is, multiply the resistors and divide over the sum of the resistors.
The mixed resistor association is the set of associations in series and in parallel. To calculate the equivalent resistance in the mixed association it is necessary to analyze the circuit and then apply the formula of the association in series or in parallel according to the need of each circuit.
Mixed resistor association issue
Now that we have explained the basics of resistor association, let’s put into practice what we have learned, the question is:
(FEEDSON DE QUEIROZ – CE) Three resistors of resistance 300 ohms each are available. To obtain a resistance of 450 ohms, using the three resistors, how should we associate them?
The alternatives are:
A) Two in parallel, connected in series with a third.
B) The three in parallel.
C) Two in series, connected in parallel with the third.
D) The three in series.
What is the correct alternative? Leave here in the comments which alternative you would choose and why.
We know that there are three types of possible resistor association, in series, parallel and mixed. To resolve this issue we will start by performing the association of resistors in series.
First trick, make a drawing with the resistors in series, to help when calculating the equivalent resistance. According to a trick, resistors in series the resistance increases, so we must add the resistance of each resistor, as in the example below.
We found that the equivalent resistance of series resistors is 900 ohms, so we know that alternative D is wrong.
Now we are going to associate resistors in parallel. Third mallet, several resistors in parallel, the equivalent resistance is less than the smallest of the resistors, as we can see in the example below.
Fourth trick, two resistors with the same resistance in parallel the final resistance is half, as we can see in the example below.
We know then that it is not possible to obtain an equivalent resistance greater than 300 ohms with the resistors in parallel, so alternative B is wrong.
It was not possible to find the answer to the question with the association of series and parallel resistors. Thus, leaving only the mixed resistor association, the question has two alternatives of mixed resistor associations, two resistors in parallel, connected in series with the third resistor or two resistors in series, connected in parallel with the third resistor.
Alternative C, two in series, connected in parallel with the third. The two resistors in series just add up, so the result is 600 ohms. The 600 ohm parallel to the third 300 ohm resistor, the equivalent resistance is less than 300 ohms so alternative C is wrong, remember the third trick.
Alternative A, two in parallel, connected in series with the third. As the two resistors of 300 ohms in parallel are the same, the result is 150 ohms, remember the fourth trick. Connected in series with the third 300 ohm resistor, just add up, so the equivalent resistance is 450 ohms.