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The form factor of sinusoidal alternating current is
1
0
11
15
11
The form factor of an alternating current (or voltage) waveform is defined as the ratio of its Root Mean Square (RMS) value to its Average value. For a perfectly sinusoidal waveform, this ratio is a constant value approximately equal to 1.11.
The form factor of an alternating current (or voltage) waveform is defined as the ratio of its Root Mean Square (RMS) value to its Average value. For a perfectly sinusoidal waveform, this ratio is a constant value approximately equal to 1.11.
KfтАЛ=IavgтАЛIrmsтАЛтАЛ тАФ Definition of Form Factor
KfтАЛ=22тАЛ╧АтАЛтЙИ1.11 тАФ Form factor for pure sine wave
For a sine wave with peak value ImтАЛ, the RMS value is IrmsтАЛ=2тАЛImтАЛтАЛтЙИ0.707ImтАЛ. The average value (over a half-cycle) is IavgтАЛ=╧А2ImтАЛтАЛтЙИ0.637ImтАЛ. Dividing the RMS value by the average value gives 2ImтАЛ/╧АImтАЛ/2тАЛтАЛ=22тАЛ╧АтАЛтЙИ1.11.
Form factor indicates the shape of the waveform relative to its average.
It is a dimensionless quantity.
A value of 1.11 is specific only to sinusoidal waves.
For a square wave, the form factor is 1.0.
Useful for calculating the peak or RMS value from average-reading instruments.
Serves as an indicator of waveform distortion.
Only applicable to periodic waveforms.
Does not provide information regarding the frequency of the waveform.
Calibration of AC measuring instruments.
Transformer design and core loss analysis.
The form factor is crucial in instrument design because most moving-coil instruments measure the average value, but require scaling to display RMS values.
Option D (1.15) corresponds to the form factor of a triangular wave.
C is correct тАФ The form factor of a sinusoidal AC waveform is mathematically derived as 22тАЛ╧АтАЛ, which evaluates to approximately 1.11.
Remember: 1.11 for Sine waves, 1.0 for Square waves, and 1.15 for Triangular waves. This pattern is a frequent target for memory-based questions in electrical engineering exams.