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An in-depth explanation of the fundamental concepts of period, frequency, and amplitude in the context of sinusoidal waveforms. It covers the mathematical relationship between these parameters, the calculation of instantaneous values, and the derivation of the RMS voltage. The document also includes a practical example of calculating the RMS voltage, frequency, and instantaneous value of a sinusoidal waveform.
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IC DEPARTMENT 1
AIM: Obtain various parameters related to given A.C. waveform. APPARATUS: Function Generator CRO CRO Probes THEORY: Whether the waveform is uni-directional, bi-directional, periodic, non-periodic, symmetrical, non-symmetrical, simple or complex, all electrical waveforms include the following three common characteristics: Period: – This is the length of time in seconds that the waveform takes to repeat itself from start to finish. This value can also be called the Periodic Time, (T) of the waveform for sine waves, or the Pulse Width for square waves. Frequency: – This is the number of times the waveform repeats itself within a one second time period. Frequency is the reciprocal of the time period, (ƒ = 1/T) with the standard unit of frequency being the Hertz, (Hz). Amplitude: – This is the magnitude or intensity of the signal waveform measured in volts or amps. Periodic waveforms are the most common of all the electrical waveforms as it includes Sine Waves. The AC (Alternating Current) mains waveform in your home is a sine wave and one which constantly alternates between a maximum value and a minimum value over time. The amount of time it takes between each individual repetition and cycle of a sinusoidal waveform is known as its “periodic time” or simply the Period of the waveform. In other words, the time it takes for the waveform to repeat itself. Then this period can vary with each waveform from fractions of a second to thousands of seconds as it depends upon the frequency of the waveform. For example, a sinusoidal waveform which takes one second to complete its cycle will have a periodic time of one second. Likewise a sine wave which takes five seconds to complete will have a periodic time of five seconds and so on.
IC DEPARTMENT 2 So, if the length of time it takes for the waveform to complete one full pattern or cycle before it repeats itself is known as the “period of the wave” and is measured in seconds, we can then express the waveform as a period number per second denoted by the letter T as shown below. Units of periodic time, (T) include: Seconds (s), milliseconds (ms) and microseconds (μs). If we take the reciprocal of the period, (1/T) we end up with a value that denotes the number of times a period or cycle repeats itself in one second or cycles per second, and this is commonly known as Frequency with units of Hertz, (Hz). Then Hertz can also be defined as “cycles per second” (cps) and 1Hz is exactly equal to 1 cycle per second. Both period and frequency are mathematical reciprocals of each other and as the periodic time of the waveform decreases, its frequency increases and vice versa with the relationship between Periodic time and Frequency given as. Relationship between Frequency and Periodic Time
IC DEPARTMENT 4 The instantaneous voltage Vi value after a time of 6ms is given as: Note that the angular velocity at time t = 6ms is given in radians so we have to convert this into an equivalent angle in degrees and use this value instead to calculate the instantaneous voltage value. The angle in degrees is therefore given as:
IC DEPARTMENT 5