A few cycles at a periodic current waveform and shown in the figure. determine the effective value of the current

General
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a few cycles at a periodic current waveform and shown in the figure. determine the effective value of the current.

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Determining the Effective Value of the Current:

To determine the effective value of the current from the given waveform, you need to calculate the Root Mean Square (RMS) value of the waveform. The effective (RMS) value of a periodic waveform is the DC voltage or current that would produce the same amount of heat in a resistor as the actual waveform over a complete cycle.

Here’s how you can calculate the effective value of the current from the provided waveform:

  1. Measure the Peaks: Identify the peaks of the current waveform. Measure the peak values accurately on the waveform.

  2. Calculate the RMS Value: The formula to calculate the RMS value of a waveform is given by:

    [ I_{\text{eff}} = \frac{1}{T} \sqrt{\int_{0}^{T} i(t)^{2} dt} ]

    Here, ( i(t) ) represents the current waveform function, and ( T ) is the time period of the waveform.

  3. Square and Average: To simplify the process, square the function of the waveform, calculate the area under the curve over one complete cycle, and then take the square root of the average value.

  4. Final Calculation: Calculate the effective value of the current by plugging in the squared function and integrating it over a complete period. Then, take the square root of this result to find the effective value of the current.

By following these steps and using the given waveform data, you can accurately determine the effective value of the current.