Understanding and Sketching a Sinusoidal Signal: A Guide to the Expression VT 24 sin 6.28t - 30°

When dealing with sinusoidal signals in electrical engineering, it is important to understand the key components that define such a signal. In this article, we will explore the expression VT 24 sin 6.28t - 30° and break down its key parameters: amplitude, phase angle, and frequency. We will also provide a step-by-step guide on how to sketch this signal on a graph sheet.

Understanding the Expression

The given expression, VT 24 sin 6.28t - 30°, represents a sinusoidal signal. Let's break it down:

Amplitude: The amplitude of the signal is 24 units. This refers to the peak value of the signal. Frequency: The frequency is given by the coefficient of t inside the sine function, which is 6.28. This can be equated to 2pi f. Therefore, we have:

[2pi f 6.28]

[f frac{6.28}{2pi} 1 text{ Hz}] Phase Angle: The phase angle is -30°, which can be converted to radians as follows:

[-30° -frac{30pi}{180} -frac{pi}{6} text{ radians}]

Graphing the Signal

To plot the signal on a graph sheet, follow these steps:

Set up the axes: The horizontal axis (x-axis) represents time (t), while the vertical axis (y-axis) represents the value of the signal (Vt). Mark the amplitude: The maximum and minimum values of Vt will be 24 and -24, respectively. Mark these on the y-axis. Mark the phase angle: The phase angle of -30° means the sine wave is shifted to the right. Start your time axis at -30° or -5 radians (since ( frac{pi}{6} frac{pi}{6} times frac{180}{pi} 30)). Draw the sine wave: Plot the points for the sine function, ensuring that the wave starts at -30° and completes one full cycle in 1 second.

Example Sketch

The following is a rough sketch of the signal VT 24 sin 6.28t - 30°:

Note: The actual sketch will vary depending on the scale of your graph sheet, but the principle remains the same.

Conclusion

Understanding the key parameters of a sinusoidal signal such as amplitude, phase angle, and frequency is crucial for analyzing and working with such signals in electrical engineering. By following the steps outlined in this guide, you can easily sketch the given signal on a graph sheet. This skill is not only essential for conceptual understanding but also for practical applications in various fields.

Further Reading

For more in-depth information on sinusoidal signals and their applications, consider exploring the following resources:

Electrical Engineering Encyclopedia Time Domain Signals Frequency Domain Analysis

By delving into these resources, you can enhance your knowledge of sinusoidal signals and their practical applications in the field of electrical engineering.