Analysis of AC Fundamental | What is AC Fundamental | Faraday law | Form Factor | Peak factor | Maximum value | Average value | Instantaneous Value | Types of induced EMF | Dynamically-induced EMF | Statistically induced EMF | Self-induced EMF | Mutually-induced EMF | Instantaneous value
Most of the time, we use alternating current to transfer power. This type of current is very suitable in every aspect. So now we will discuss AC fundamentals.
What is AC Fundamental?
In this heading, we will discuss many topics like the Faraday law of electromagnetics, types of emf, various types of alternating current, and various types of factors.
Faraday’s law of electromagnetic induction
As seen in the illustration, there is a one-turn coil with two conductors, a and b. There are also two coil sides. However, the coil side has always remained two, unless your coil’s turn has increased.
What is electrical circuit and why it is so important?
So, one turn of a coil has two conductors. It means that our conductor’s number is two times the time of the coil’s turn.
Number of conductors = 2 * no. of Turn
Faraday’s first law
There is a coil with N turn and flux is ɸ. Figure is given below. Suppose that flux is passing through the coil, and the resultant flux linkage will be N ɸ.
Now, according to the Faraday law, in a coil of flux, the linking process will change with time. Then an EMF will be induced at the coil’s two ends. This EMF is dependent on the rate of change of the flux linkage. If, in this situation, a load resistance is connected at both ends of the coil, a current will flow through it.
This current is in direct opposition to the reason for which it exists. It means this current opposes the rate of change of the flux linkage. To oppose the rate of change of flux linkage, a coil behaves like a magnetic coil and opposes the changes in flux in the coil.
Note: For this current, which is flowing through the load, the current direction will be decided on the basis of Lenz law.
The second law of faraday is:
The duration of the flux change in the coil emf will be determined in this manner.
e = – Nd ɸ/dt
where e is the emf of the coil. Above emf can also be written as follows:
e = -d (N ɸ)/dt
where N ɸ is flux linkage. This negative sign comes from the Lenz law.
Types of induced EMF in AC fundamental:
Basically, there are two types of induced EMF.
- Statistically induced EMF
- dynamically induced EMF
When there is motion between the coil and the field flux, dynamically induced EMF is produced. Consider how an alternator or generator works on the principle of dynamically induced emf.
Statistically induced EMF:
The induced emf is called statically induced emf if there is no motion between the coil and the field flux. Statistically induced EMF can be classified into two types.
- Self-induced Emf
- Mutually induced EMF
If a coil induces EMF due to its own flux changes, this is called self-induced EMF. The auto-transformer works on the principle of self-induced EMF.
If a coil induces EMF due to neighbouring coil flux changes, this is called mutually induced EMF. Except for auto-transformers, almost all types of transformers operate on this principle.
Note: A transformer’s efficiency is 98%, which is very high. Because a transformer contains no moving parts, The operating principle of an induction motor is the same as that of a transformer. But the efficiency of the induction motor is 85 percent. The main reason is that the induction motor has moving parts like a rotor. Because it is a rotor, there is a proper air gap, which reduces the motor’s efficiency.
Different values of alternating quantities:
There are many types of values regarding alternating quantities.
- Instantaneous value
- Maximum, maximum, peak, or crest value
- Average value.
- RMS value
The value of alternating quantities at any instant is called their “instantaneous value.”
Maximum value, peak value, or crest value:
This is the maximum instantaneous value of alternating quantities.
To determine the average value of any alternating quantity signal, we must first determine the signal’s period. And then we find out the area of the signal. And then we divide the area of the signal by time period. The resultant value is a average.
Rrectangular waveform signal is given above. In this way, we can see that the time period of the signal is two units. Because the signal cycle is completed after two units, and the process is repeated. After that, we find out the area of the signal. As can be seen, only one rectangular shape is formed in a single time period. which is 0 to 1, and 1 to 2 indicates zero. So, according to the formula for the area of a rectangular shape, the total area is 2 units. These 2-unit is divided by time period, which is also 2-units. So, the resultant value is 1 unit.
Average value: (2×1+1) /1 = 1.
If the signal is symmetrical, to find the average value, the time period is half of the cycle.
If there is any signal that is unsymmetrical, an unsymmetrical signal is defined as a constant value with a symmetrical value. So, the average value of an unsymmetrical waveform is the constant value of a signal.
As you can see in the signal equations of alternating quantities, there is a constant value of 10 and a symmetrical value of 10sinωt. This is an example of an unsymmetrical waveform. So, the average value of the waveform is 10, which is the constant value of the unsymmetrical waveform.
i = 10 + 10sinωt
10 = constant value.
10sinωt= symmetrical value
PMMC-type instruments read only the average value of the signal.
What is the RMS value?
Initially, to find out the RMS value of any signals, we found out the average value of the signal. And then we keep the resultant value under root. RMS value is the final resultant value.
The full form of RMS value is root mean square value.
The RMS value is always greater than the average value, instead of rectangular waveforms. In the case of a rectangular waveform, the RMS value and average value are the same.
- A moving iron instrument reads only the RMS value of the signal.
- In the case of a direct current signal, the average, RMS, and maximum values are all the same.
Different factors of alternating quantities:
In spite of different values, there are also some factors affecting the alternating quantities.
- Form factor
- Peak or crest factor
The ratio of the RMS value to the average value known as the form factor
RMS value or average value = form factor
Significant form factor:
- The form factor justifies the shape of any waveform.
- As we know, we transmit the power at different levels of voltage, like 11 kV, 33 kV, 66 kV, 132 kV, and 220 kV. This voltage level is the multiplier of 11 KV. Form factor decides these voltage levels.
Peak or crest factor:
The peak factor, or crest factor, is the ratio of the maximum value to the RMS value.
Peak factor = maximum value/RMS value
Significant peak factor:
The peak factor or crest factor indicates the material’s dielectric strength. And here is the example, the dielectric strength of air at NTP is 3 KV/mm. This 3 KV is the peak value.
Different values for different types of signals:
|TYPE WAVE||AVERGE VALUE||RMS VALUE||FORM FACTOR||PEAK FACTOR|
|SINUSOIDAL WAVE||2Vm/ π||Vm/√2 = 0.707||1.11||1.414|
|HALF WAVE RECTIFIER SIGNAL||Vm/π||Vm/2||1.57||2.0|
|FULL WAVE RECTIFIER SIGNAL||2Vm/ π||Vm/√2 = 0.707||1.11||1.414|