Standard Terminology of AC Voltage Waveform - AC Circuits - Basic Electrical Engineering

Summary

This video explains key terms related to AC voltage waveforms, focusing on sinusoidal waveforms. It begins by revisiting Faraday's law of electromagnetic induction and describes how AC voltage changes in magnitude and direction over time. Key terms defined include instantaneous value, amplitude (the maximum value), cycle, time period (T), and frequency (F). The relationship between time period and frequency is discussed, along with angular frequency (ω = 2πF). Finally, the video presents the AC voltage equation and explains how various quantities are represented within one cycle of the waveform.

Takeaways

• 🔄 The AC voltage waveform is sinusoidal and follows Faraday's law of electromagnetic induction.
• ⚡ Instantaneous value refers to the AC voltage at a specific point in time.
• 📈 Amplitude is the maximum value attained by the AC voltage, whether positive or negative.
• 🔁 A cycle is the complete repetition of positive and negative values in the AC voltage waveform.
• ⏳ Time period (T) is the time taken for one complete cycle of the AC waveform, measured in seconds.
• 🎚 Frequency (F) refers to the number of cycles completed per second, measured in Hertz (Hz), and is inversely related to the time period (T).
• ⏰ Angular frequency (ω) represents frequency in angular terms and is calculated using the formula ω = 2πF, measured in radians per second.
• 📐 The AC voltage waveform can be expressed using the equation e = Em sin(ωt), where Em is the amplitude, and ω is the angular frequency.
• 🔄 The waveform repeats itself over time, with values of instantaneous voltage, amplitude, and time period being clearly defined.
• 🔢 The angular frequency (ω) can also be related to time period T using the formula ω = 2π/T.

Q & A

What is the instantaneous value of an AC voltage?

The instantaneous value of an AC voltage is the value of the voltage at a specific point in time. Since AC voltage changes with both magnitude and direction over time, this term refers to its exact value at any given instant.

What is amplitude in an AC waveform?

Amplitude is the maximum value that an AC voltage waveform can attain, either in the positive or negative direction. It represents the peak value of the waveform.

What is a cycle in an AC waveform?

A cycle is a complete set of positive and negative instantaneous values in an AC waveform. It includes one full wave starting from zero, reaching the maximum positive value, returning to zero, and then reaching the maximum negative value before returning to zero again.

How is the time period of an AC waveform defined?

The time period is the duration taken by an alternating quantity to complete one full cycle. It is denoted by the capital letter 'T' and is measured in seconds.

What is frequency in the context of an AC waveform?

Frequency is the number of cycles that an AC voltage completes in one second. It is denoted by 'F' and measured in Hertz (Hz). The relationship between frequency and time period is F = 1/T.

What is angular frequency, and how is it related to frequency?

Angular frequency, denoted by 'ω', represents the frequency in angular terms, typically in radians per second. It is related to the standard frequency by the formula ω = 2πF, where F is the frequency in Hertz.

How is the angular frequency (ω) derived from time period (T)?

Angular frequency can also be expressed in terms of the time period using the formula ω = 2π/T. This relates angular frequency to how long it takes for one complete cycle to occur.

What is the general form of an AC voltage waveform equation?

The general form of an AC voltage waveform equation is e = Em sin(ωt), where 'e' is the instantaneous value of voltage, 'Em' is the amplitude, 'ω' is the angular frequency, and 't' is the time.

How is the equation for an AC voltage waveform modified in terms of frequency?

In terms of frequency, the AC voltage waveform equation is written as e = Em sin(2πFt), where 'F' is the frequency and 't' is the time. This shows how the waveform changes based on frequency.

What does the graph of an AC waveform represent?

The graph of an AC waveform represents how the instantaneous value of voltage changes over time. It shows the sinusoidal nature of the waveform, with peaks corresponding to the maximum and minimum values, and the time period (T) is the duration for one full cycle.