If you are studying electrical engineering, either in high school or at the university, you will surely want to learn how you can calculate impedance, since it is essential to pass this subject.
The direct current circuits are quite simple and I’m sure anyone has passed them without problems, however, then comes the dreaded alternating current, which is for many the most difficult part of the course.
Alternating current adds the element of magnetic fields, creating a current that fluctuates, instead of a current that is followed in a circuit like direct current. For this reason, we have a current that is very difficult to explain if you are not an expert.
In this case, impedance is usually something that is asked a lot in problems and it is necessary to learn to pass. Also, not only do you have to know a simple formula, but before you can get to this, you must master the calculation of other circuit elements, since you will need them to perform this formula.
In addition, you will also have to handle things like complex numbers, something that is certainly not that easy. Of course, once you learn how to do it, you will be able to solve all problems practically enough. Practice is what works and makes perfect, so once you learn, it’s your turn to practice and do the exercises that the teacher sends you.
We will teach you not only the impedance formula and how it is calculated, but we will also teach you how to calculate all the necessary data to be able to solve the formula correctly. We will also teach you its definition, what it is for and why an impedance must be calculated in an alternating current circuit.
Instructions for calculating impedance
- Know what impedance is: Impedance is a characteristic that is only found in alternating current electricity circuits, that is, you will not find it in direct current. In an electrical circuit, it is measured in ohms and is represented by a letter Z. Its definition is really similar to that of resistance in direct current, that is, its resistance, but adding the element of reactance as well, something that we will explain later. In a circuit, it is necessary that there are impedances to achieve a balance of current and that there is not too much current. In this case, the impedance is not as simple as in direct current, since here we have to look at both resistance and reactance, both with inductors and capacitors, to calculate the impedance.
- Resistance: The resistance is the same as that of direct current, since it is simply a question of stopping the current . In this case, we have to look at the resistors.
- Reactance: Reactance is a special type of resistance, but instead of being based only on material, it is based on magnetic fields. Here there are two types of elements that perform it, which are inductors and capacitors.
- Calculate the resistance: This is the easiest part of the problem, since all we have to do is calculate the resistances that are in the circuit. For this we resort to Ohm’s law, that is, voltage is equal to current times resistance. If we solve the equation, we pass the current to divide, so we have to divide the voltage by the current to calculate the resistance. Another way is to add the resistances, as long as we have the data and in a real circuit, we have to use a multimeter to make sure that we have done the operations correctly.
- Add the reactance to calculate the total: Now it is time to calculate the reactance, something that is not so simple, since in addition to being generated only in alternating current, it depends a lot on the reactance of the inductors, of the capacitors and if they are in series, or if they are in parallel.
- Series inductors only: Inductors or coils are what create a magnetic field to oppose changes in direction. To calculate the inductive reactance in series, we must carry out the formula that inductive reactance is equal to two times the number pi, times the frequency of the circuit in hertz times the inductance of the circuit in henries. So, the more frequency, the more induction. If they are in series, we must calculate each inductive reactance and add without problems.
- Only inductors in parallel: If it is in parallel, the procedure is the same, but the inverse is added, that is, instead of adding x1+x2, we add 1/x1+1/x2 and this in turn becomes the inversely, leaving 1/(1/x1+1/x2).
- Only capacitors in series: Capacitors are elements that are responsible for storing an electrical charge, which enters and leaves it to oppose the current in the correct way. In this case, the capacitor reactance is inversely proportional to the inductor, since if the other is directly proportional to the frequency, here it is inversely proportional. The formula is practically the same as the previous one, but in reverse and changing the inductance for the capacitance, which is measured in farads. In the end, the capacitor reactance is equal to the inverse of two times pi, times the frequency and times the capacitance. As with the inductor, we must add all of them if they are in series.
- Only capacitors in parallel: As before, we must calculate each one in the same way as in series, but add the inductive one as we have added in parallel.
- Subtract inductive and capacitive reactance to calculate the total: Now we are going to calculate the total reactance, which we are going to call X. For this we only have to subtract the inductive reactance, minus the capacitive, which we have calculated previously. This will give us the total reactance, which we will add to the resistance to calculate the impedance.
- Calculate the impedance: Now it is time to calculate the impedance, which after a long way, we can already calculate. We are going to need the total reactance that we have just calculated, having previously calculated the inductive and capacitive reactance of each device and we will also need the resistance of the alternating current circuit. To solve this, we are going to use geometry, since all this ends up forming a right triangle.
- In series we apply the Pythagorean theorem: Z=√(R 2+x 2 ): We are going to take advantage of the laws of geometry to form a right triangle. Here, we have the hypotenuse which is the impedance Z, the first leg which is the resistance and the second which is the reactance. Applying the Pythagorean theorem, we must square the legs and then take the root to find the hypotenuse, which is the reactance.
- In parallel, with complex numbers: Z= R+jX: In the case that we are in parallel, we must use complex numbers, which are already at the university level. In this case, the formula is Z=R+jX, where j is the complex number. This is because it is an imaginary element, but the R is a Real component. So we will calculate the impedance by simply doing the formula and leaving the j indicated. For example, if the R is 5 and the X is ½, we will have to indicate Z=5+1/2j, leaving it like that. We must always use j, since i is used in alternating current for current in an operation that is irrelevant.