Chapter 3

AC voltage

We have already seen the components liabilities and their behavior in DC. Since the behavior of these varies when treating them in DC or AC voltage deserves a separate paragraph the discussion on the behavior of these elements when it is put under them the circulation of an alternated current.

Before beginning it agrees to also observe the difference of this type of current with the DC and the explanation of the important parameters but of an alternating signal.

The DC is that one that maintains its value of constant tension and without change of polarity, example of her can be a battery of which they are used in the automobiles or the batteries with which we fed our toys or electronic calculators. This type of current is known it like C.C or, according to the authors of English speech, D.C.

The AC voltage also maintains a difference of constant potential, but its polarity varies with time. Usually denominates it a.c. or A.C in English.

Important parameters of the AC voltage:

Frequency: Number of times that an AC voltage changes of polarity in 1 second. The unit of measurement is Hertz (Hz) and is designated it with letter F. Of this form if in our home we have a 220 tension of V 50 Hertz, means that this tension will have to change to its polarity 50 times per second.

One more a more rigorous definition for the frequency: Number of complete cycles of a.c. that happen in the time unit.

Phase: It is the fraction of cycle passed from the beginning of the same, his symbol is Greek letter q.

Period: It is the time that takes in taking place a complete cycle of a.c. denominates T. In our example of a tension of 220 V 50 Hertz its period is of 20 mseg.

The relation between the frequency and the period is F=1/T

Instantaneous value: Value that takes the tension at every moment from time.

Maximum value: Value of the tension in each “crest” or “valley” of the signal.

Average value: Arithmetic mean of all the instantaneous values of the signal in a given period.

Its mathematical calculation takes control of the formula:

Effective value: Value that produces the same effect that equivalent signal C.C. One calculates by means of:

Value tip to tip: Value of tension that goes from the maximum to the minimum or of a “crest” to a “valley”.

In the following figures we see an alternating signal where some of these parameters have been specified, the figure a) shows an alternating wave where the effective value, the maximum value, the value tip to tip and the period are seen so much. In figure b) we see two waves alternating, of equal frequency, but been out of phase 90º.

In the figure a) if the frequency is of 50 then Hertz the period is T=20 mseg and will include from the origin to point D. In her also the phase can be seen, the one that is measured in angular units, or in degrees or radianes. Also we can see the different points where the short signal from the axis of the time graduated in radianes.

In figure b), as we said already it, two alternating signals been out of phase 90º are seen (p/2 radianes), that is to say, when the first signal starts of the point To, second does from point B, being the desfasaje it enters the points and B of 90º. Therefore one says that we to each other have two signals of equal been out of phase frequency and amplitude but by 90º.

With the sight until now we can to present/display to a sine signal in its typical representation:

U = Umax sen (2pft + q)

Other types of AC voltage:

In electronics they are used infinity of types of signals thus is made practically impossible to enumerate them to all, but we will make reference to most common, after sine and continuous the pure one.

One of them is pulsatoria (also call square wave). This wave is seen in the following figure:

Another frequently used wave in electronics is the triangular wave:

and also it is the wave tooth of mountain range:

It is possible to clarify that the definitions of the parameters that became for a sinusoidal wave maintain valid for these types of waves.

Behavior of the components liabilities in C.A:

The components liabilities have different behavior when two currents of different nature are applied to them, one alternating and the other continuous one.

The answer in C.C we analyzed already it, remains to us to analyze the answer of these elements in a.c.

Resistencias and C.A: These are the unique elements liabilities for which the answer is the same as much for a.c. as for C.C.

One says that in a resistance the tension and the current are in phase.

Inductancia and a.c.: To this type of component we have not made reference when we dealed with to the elements in given C.C its similar behavior to the resistance in that type current. However in a.c. its answer varies considerably

The signals tension and current maintain the same waveform but no longer they are in phase but been out of phase 90º. The current retards 90º with respect to the tension.

The parameter that measures the value of the inductance is the inductive reactance:

XL = 2 p f L where XL are expressed in ohms

and as XL = V/I by the Law of then Ohm we have:

i (t) = V (t) /XL = V (t) /2pfL

Where we can see that now the current does not depend exclusively on the value of the tension and the inductive reactance, but also of the frequency, being inversely proportional to this.

Capacidad and C.A: In the figure we see the connection of a capacity a circuit of a.c.

It is now the case in which the current goes ahead 90º with respect to the tension, maintaining the same waveform that this one.

The calculation of the capacitive reactance (measured in ohms) takes control of the following formula:

XC = 1/2pfC

and applying the Law of Ohm again:

i (t) = V (t)/XC = 2pfC V (t)

Also the current depends here on the frequency, but now he is directly proportional to this one.

Impedance: 

A factor that appears in alternating is the impedance. This is moderate in ohms and it is defined:

Z = R + j (XL - XC)

To the being a complex value (vectorial sum), is moderate its module and phase:

The inverse one of the impedance denominates admittance (y) and it is defined:

And = 1/Z

Combinations R-L, R-C and RLC:

Besides the cases already seen where they were only present in a circuit a single type of passive element, cases exist in which resistance with capacitores and inductancias are combined, we will see how the currents and tensions in each of these combinations behave.

R-L:

In the graph we can see the vectorial diagram of the tensions of the circuit. We see how VR is in phase with the current, VL is advanced 90º with respect to this and then solving the vectorial sum we see that VT is advanced to degrees to the current.

R-C:

In the same way that in circuit R-L we see in the vectorial diagram of the tensions of the circuit, as again VR is in phase with the current, whereas VC are 90º slow to the current. Of the vectorial sum we see that VT is to degrees slow with respect to I.

R-L-C:

Finally we will see the case in which the 3 types of components liabilities are present in a circuit of a.c. (R, L, C).

The impedance (z) calculates since already we have seen.

In the vectorial diagram of the tensions in the circuit we see VC slow 90º current, VR in advanced phase with her and VL 90º. Nótese that in the figure did not draw total the resulting tension since this one is function of the three present tensions, being the total tension (VT) advanced to the current if XL > XC, slow if XC > XL and will be in phase with the current if XC = XL.

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