Question

What is the relation between frequency and time period in AC circuits?

Answer 1

In AC (alternating current) circuits, frequency and time period are closely related parameters that describe the characteristics of the AC waveform. Let's break down their relationship:

Frequency (f): Frequency is the number of complete cycles (oscillations) of an AC waveform that occur in one second. It is measured in Hertz (Hz). In other words, frequency indicates how many times the waveform completes a full cycle in a given time frame. Mathematically, frequency is the reciprocal of the time period.

Formula:


=
1

f=
T
1
    ​


where:


f = Frequency in Hertz (Hz)

T = Time period in seconds (s)

Time Period (T): Time period is the time taken for one complete cycle of an AC waveform to occur. It is measured in seconds (s). Time period represents the duration it takes for the waveform to repeat its shape.

Formula:


=
1

T=
f
1
    ​


where:


T = Time period in seconds (s)

f = Frequency in Hertz (Hz)

So, frequency and time period are inversely proportional to each other in AC circuits. As the frequency increases, the time period decreases, and vice versa. This relationship holds true for all AC waveforms, whether they are sinusoidal, square, triangular, or any other shape.

For example:

If the frequency of an AC waveform is 50 Hz, the time period would be
1
50
50
1
    ​

 seconds or 20 milliseconds.
If the frequency of an AC waveform is 1000 Hz (1 kHz), the time period would be
1
1000
1000
1
    ​

 seconds or 1 millisecond.

This relationship between frequency and time period is fundamental in understanding the behavior of AC circuits and is used in various calculations involving AC circuit analysis, design, and troubleshooting.