Fundamentals of Alternating Current

Alternating current may be defined as the current whose magnitude and phase changes with time.

So, we can alternating current as:

According to above figures we can  have four basic types of alternating currents i.e. sinusoidal and non-sinusoidal alternating currents. Non-sinusoidal sine wave includes triangular, square and saw tooth alternating currents.

The image below shows a sinusoidal alternating current

Sinusoidal Alternating Current

Terminologies in AC:

Cycle: An alternating current starts from zero, reaches to positive maximum value. Then it attains negative maximum after crossing zero and then again reaches zero from where it will again attain the positive value. When AC starts from zero, attains maximum value and then again reaches zero, this is known as positive half cycle. Now from the zero of end of positive half cycle its value again starts increasing but this magnitude is negative. It attains the negative maximum value and then again attains the zero value. This is known as negative half cycle. The complete set of one positive half cycle and negative half cycle is known as a cycle.

2. Time Period: It is the time duration required for the quantity to complete one cycle. "T" is used to represent the time period. Time may be in second, millisecond etc.

3. Frequency: It is the number of cycles in  one second. Its unit is " Hz " . For example if a quantity has frequency of 10 Hz then there will be 10 cycles in one second.

4. Peak Value or maximum value: It is the maximum value that a quantity attains in a cycle. This may be positive or negative. So, AC has one positive maximum and one negative maximum in one cycle. It is represented by the quantity with subscript "m" e.g. I_m
In this, "I" represents current and "m" represents the maximum value. So if   I_m= 10 A, it represents the maximum value of current.

5. Instantaneous Value: It is value of the quantity at any instant of time.

6. Average Value :  It represents that steady current that transfers same amount of charge to a circuit in  a given  time interval as is transferred y the alternating current to the same circuit in same duration. The average value over one complete cycle is zero. It is represented by I_AV

7. RMS ( root mean square ) Value / Effective Value : It is that steady current which produces same quantity of heat, when flows through a resistor of known resistance for a given period of time as produced by the alternating current when flows through the same resistor for the same period of time.
It is represented by I_rms

Mathematically,

I_AV = 0.637 * I_m

I_rms = 0.707 * I_m

I_AV = 0.9 * I_rms

The table below may be effective for the conversion:

Mathematical representation of sinusoidal AC:

i = I_m sin Θ

The concept of above expression can be interpreted as:

A complete cycle of a sinusoidal waveform is of 360 degree. So for every value of Θ, the instantaneous value of sinusoidal AC will change. In other words, the instantaneous vale is a function of Θ. So to get instantaneous value of a sinusoidal AC, the value of Θ is required.

E.g. If I_m = 10 A, and we need to know the value of current at Θ = 30..

So the instantaneous value of current is:

i= 10*sin30 = 5 A.

8. Phase of AC : It represents the position of a point in time (instant) on a waveform cycle. E.g. if a sinusoidal waveform has a time period of 10 seconds then 1sec, 2 sec etc. may be phase of a sinusoidal waveform.

9. Phase angle : It the equivalent of phase represented in angle. The figure below shows the relationship between phase and phase angle of AC.

Now the mathematical and graphical interpretation  of AC can be :

10. Angular frequency (ω) :