In this article, we will discuss the basic terms related to **AC (Alternating Current) circuits**.

Knowledge of this terminology is very important to study
AC circuits. Hence, every electrical engineering student and professional must
know the meaning of these basic terms of AC circuits.

In the upcoming sections of this article, we will discuss
the following six major terms related to ac circuits:

- Waveform
- Cycle
- Time Period
- Frequency
- Phase Angle
- Phase Difference

Now, let us discuss these terms of AC circuits in detail one by one.

# (1). Waveform:

The curve or graph obtained by plotting instantaneous values
of an AC quantity (current or voltage) against time is called the **waveform** of the AC quantity.

Consider a sinusoidally varying alternating voltage
expressed by,

The waveform of this alternating voltage
is shown in figure-1 below.

# (2). Cycle:

One complete set of positive and negative
instantaneous values of an alternating wave is called a **cycle**. In other words, one complete set of alterations is called the cycle of the ac wave. One complete cycle of the alternating voltage (*v*) is shown in figure-1 above.

Here, in one complete cycle, there are
two half cycles, i.e. one positive half cycle and one negative half cycle.

# (3). Time Period:

The time taken to complete one cycle by
the AC wave is called its time period. The time period is usually denoted by T.

For the AC wave shown in figure-1, the time
period is equal to 2Ï€.
In other words, for a sinusoidal ac wave, during one time period T, the change
in the angle of the wave is equal to 2Ï€. Therefore,

`\Î¸=Ï‰T=2Ï€`

`\∴T=(2Ï€)/Ï‰`

The time period is measured in seconds (s).

# (4). Frequency:

The number of cycles completed by the AC
wave in one second is called the **frequency**
of the AC wave. Frequency is denoted by “*f*”.

The ac wave shown in figure-1, one cycle
is completed in T seconds. Therefore, in 1-second 1/T cycles will be completed.
Hence, the frequency is given by,

Frequency is measured in **cycles per second (c/s)**. The SI unit of
frequency is **Hertz (Hz)**.

Since, we have,

Therefore, the frequency can also be
given by,

Thus, the relationship between angular
frequency (Ï‰)
and linear frequency (f) is given by,

Where the angular frequency Ï‰ is measured in radians per second.

# (5). Phase Angle:

The
angle of an AC wave at t = 0 is called the **phase
angle of the AC wave**. For example, consider an ac wave expressed by the
following expression,

At
any instant of time (t), the angle of the wave is equal to (Ï‰t + Ï•). But at t =
0, we have, the angle of the wave equal to Ï•. Therefore, Ï• is called its phase
angle.

# (6). Phase Difference:

The
angular separation between the zero crossing points of two ac waves is called
the **phase difference** between them.

Let
us consider three sinusoidal current waves of the same magnitude,

`\i_1=I_m sinÏ‰t`

`\i_2=I_m sin(Ï‰t+Î¸_1)`

`\i_3=I_m sin(Ï‰t-Î¸_2)`

The
waveform representation of these currents is shown in the figure-2 below.

_{1}starts at t = 0, thus, it may be taken as the

**reference wave**.

By
definition, the angular distance between zero crossing points of two waves is
called phase difference. Thus, the angle Î¸_{1} is the phase difference
between i_{1} and i_{2}, and Î¸_{2} is the phase difference
between i_{1} and i_{3}.

The
phase difference between two ac waves can be numerically computed by finding
the difference in the phase angles of the two waves.

For example, from the figure-2, we have,

Phase
difference between i_{2} and i_{1} = Î”Î¸ = Î¸_{1} – 0

`\⇒Î”Î¸=Î¸_1`

In general,

`\Î”Î¸=Î¸`

- If
Î”Î¸ is positive, then i
_{2}is said to be leading the current wave i_{1}by an angle of Î”Î¸. - If
Î”Î¸ is negative, then i
_{2}is said to be lagging the current wave i_{1}by an angle of Î”Î¸.

Hence, in figure-2, we can conclude,

- The
wave i
_{2}leads i_{1}by an angle Î¸_{1}. - The
wave i
_{3}lags i_{1}by an angle Î¸_{2}. - The
wave i
_{2}leads i_{3}by an angle (Î¸_{1}+ Î¸_{2}). - The
wave i
_{3}lags i_{2}by an angle (Î¸_{1}+ Î¸_{2}).

In
general, if the phase angle of an AC wave is Î¸, it is said to be leading from
the reference wave. On the other hand, if the phase angle of an AC wave is –Î¸, it is said to be lagging from the reference wave.

Therefore,
this is all about the six most important terms associated with AC circuits in
electrical engineering.