# AC Fundamentals (Alternating Current)

The current that changes its direction of flow with a certain frequency is called an alternating current. This is the reason, an alternating current circuit does not have any positive or negative terminal. This is because after reaching its maximum value in any particular direction it starts reducing to zero immediately. But to complete the circuit even in an alternating system there must be at least two conducting paths. One path through which the alternating current actually flows is called the phase. And the return path is called the neutral. Therefore the neutral actually completes the circuit.

### Advantages of Alternating Current over Direct Current

• The generation of alternating current is easier than that of direct current.
• The voltage level of an ac system can easily be stepped up and down with the help of power Transformers.
• At a high voltage level, an alternating power can be sent to a very far distance.
• The alternating current operates induction motors. An induction motor is robust, cheap and maintenance-free compared to a DC motor.

If there are two or more phases in an alternating system, it is called a polyphase system.

### Advantages of a Polyphase System over a Single Phase System

• Polyphase ac motors and generators are more efficient than single-phase ac motors or generators.
• For transmitting a certain power from one place to another, the cost of the polyphase system is much lower than that of a single-phase system for the same purpose.
• The rotation of a polyphase motor is much smooth whereas the rotation of a single-phase motor is somewhat pulsating.
• The polyphase alternating current motors are self-starting whereas a single-phase motor requires some external means to start.

#### Some Fundamental Terms used in Alternating Current Systems

If an armature rotates inside a magnetic field it produces an alternating current. The expression of alternating EMF induced in the armature can be given as Where e is the instantaneous value of the alternating current at any instant and Em it is the maximum induced EMF across the armature conductors. Omega is the angular speed of the armature expressed in radian. Lastly, t is the time of the instant at which the value of the alternating induced EMF is e(t).

#### Cycles of Alternating Current

The summation of positive and negative half-cycles is called a complete cycle. The angular distance of a complete cycle is 360 degrees. The number of complete cycles created per second in an alternating wave is termed as the frequency.

#### Time Period of Alternating Current

It is defined as the time required by an alternating wave to propagate a complete cycle or 360 degrees.

#### Relation between Time Period and Frequency

Frequency is the measure of the number of cycles formed per one second in an alternating wave. The time period is the time required to form one complete cycle. Airport bus simple relation between these two quantities is ### Frequency of Alternating Current

The number of cycles formed in one second is called the frequency. Generally, the frequency is denoted by letter f. The unit of frequency is Hertz (Hz). In India, the frequency of the alternating current is 50 Hertz. That means the alternating current completes 50 complete cycles in 1 second. Therefore the time period of the alternating current in India is 1/50 second or 20 ms.

In a generator, one armature conductor has to cross two adjacent opposite magnetic poles to produce one cycle of alternating current. So, the frequency of the generated alternating current can be determined by the number of pairs of adjacent poles crossed by the armature conductor in one second.

If N is the speed of the rotation of armature in RPM, the armature completes N/60 complete rotations in one second. Again if P is the number of poles in the generator, P/2 is the number of pairs of poles. So, the armature conductor crosses P/2 pairs of poles during its one rotation. Therefore the armature conductor crosses (N/60)X(P/2) pairs of poles during one second. This is nothing but the frequency of the alternating current produced by the generator. Therefore we can write ### Peak Value or Amplitude of an Alternating Current

The maximum positive or negative value of an alternating current is called its peak value or its amplitude.

#### Peak to Peak Value

The sum of the positive peak value and the negative peak value is called the peak-to-peak value of the alternating current.

### RMS Value of an Alternating Current

When an alternating current flows through a pure resistance for a certain time, it produces certain heat energy. The value of direct current that produces the same heat energy during the same period of time on the same resistance is known as the RMS value of the alternating current. It is the direct current equivalent of the alternating current. It is 0.707 times of amplitude.

#### Peak Factor

This is the ratio of amplitude to the RMS value of an alternating quantity. The value of the peak factor is 1/0.707.

#### Electrical Degrees

When an armature conductor crosses a pair of adjacent opposite magnetic poles in a generator, it creates a complete cycle of sinusoidal alternating current in the load. The angular progress of the wave for a complete cycle is always 360 degrees. If there are P/2 number of magnetic poles available in the generator, the armature conductor crosses a total P/2 number of poles during a complete rotation. That means the armature conductor creates a total P/2 number of complete cycles during one complete physical rotation of the armature. The total angular progress of the wave for one complete rotation of the armature conductor will be (P/2 X 360) degrees. This angular advancement of the wave is denoted and measured with electrical degrees. A complete physical rotation means 360 mechanical degrees. Therefore the simple relation between electrical degrees and mechanical degrees is as follows.

360 degrees mechanical = (P/2) X 360 degrees electrical

or

mechanical degrees = (P/2) X electrical degrees.

Let’s have an example.
Suppose, the number of poles of a generator is 4. The complete rotation of one armature conductor signifies, 360 degrees mechanical or 360 X 4/2 or 720 degrees electrical.

### Transient in AC Circuit

The sudden disturbance in an AC circuit which stays a very few moments is known as transient.
There are many reasons cause transient disturbances in an AC circuit.

1. The sudden supply to the circuit.
2. The sudden interruption of supply to the circuit.
3. The sudden change in supply voltage to the circuit.
4. Sometimes the sudden release of the stored energy in a capacitor or inductor may cause transient in the circuit.

### Phasor

This is the graphical representation of an alternating electrical quantity. The angle between two such phasors signifies the angular difference between the alternating electrical quantities represented by the phasors. This is also known as phase difference.

• There is no phase difference between voltage and current in a purely resistive circuit.
• In a purely inductive circuit, the current lags 90 degrees electrical the applied voltage.
• In a purely capacitive circuit, the current leads 90 degrees electrical the applied voltage.

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