The form factor of sinusoidal alternating current is

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Examoogle · Accepted Answer

1.11

Explanation: 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.

Working Principle: For a sine wave with peak value $I_m$, the RMS value is $I_{rms} = \frac{I_m}{\sqrt{2}} \approx 0.707 I_m$. The average value (over a half-cycle) is $I_{avg} = \frac{2 I_m}{\pi} \approx 0.637 I_m$. Dividing the RMS value by the average value gives $\frac{I_m / \sqrt{2}}{2 I_m / \pi} = \frac{\pi}{2\sqrt{2}} \approx 1.11$.

Key Formulas: $K_f = \frac{I_{rms}}{I_{avg}}$ — Definition of Form Factor; $K_f = \frac{\pi}{2\sqrt{2}} \approx 1.11$ — Form factor for pure sine wave

Key Points: 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.

Advantages: Useful for calculating the peak or RMS value from average-reading instruments.; Serves as an indicator of waveform distortion.

Disadvantages: Only applicable to periodic waveforms.; Does not provide information regarding the frequency of the waveform.

Applications: Calibration of AC measuring instruments.; Transformer design and core loss analysis.

Additional Info: 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.

Answer: C is correct — The form factor of a sinusoidal AC waveform is mathematically derived as $\frac{\pi}{2\sqrt{2}}$, which evaluates to approximately 1.11.

Exam Tip: 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.

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