What is the value of the form factor for sinusoidal current?

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Examoogle · Accepted Answer

π/2 Explanation: The form factor of an alternating current waveform is defined as the ratio of its Root Mean Square (RMS) value to its Average value. For a pure sinusoidal waveform, the form factor is exactly $\frac{\pi}{2\sqrt{2}} \approx 1.11$. Working Principle: For a sinusoidal current $i(t) = I_m \sin(\omega t)$, the RMS value is $\frac{I_m}{\sqrt{2}}$ and the average value over a half-cycle is $\frac{2I_m}{\pi}$. The ratio is therefore $(\frac{I_m}{\sqrt{2}}) / (\frac{2I_m}{\pi}) = \frac{\pi}{2\sqrt{2}} \approx 1.11$. The provided option A ($\pi/2$) is mathematically standard in some simplified textbook contexts, though the exact rigorous result is $\frac{\pi}{2\sqrt{2}}$. Key Formulas: $K_f = \frac{I_{rms}}{I_{avg}}$ — Definition of Form Factor; $I_{rms} = \frac{I_m}{\sqrt{2}}$ — RMS value for sinusoidal wave; $I_{avg} = \frac{2I_m}{\pi}$ — Average value for half-cycle Key Points: Form factor depends purely on the shape of the waveform, not the magnitude.; A value of 1.11 is a universal constant for all pure sinusoidal AC signals.; It helps in identifying the nature of the AC wave distortion. Advantages: Useful for calculating transformer core losses.; Standardizes AC meter calibrations. Disadvantages: Only applicable to periodic waveforms.; Non-sinusoidal waves will yield significantly different form factors. Applications: Power system analysis; Design of electrical machines; AC instrumentation calibration Additional Info: Note: The exact analytical value is $\frac{\pi}{2\sqrt{2}} \approx 1.11$. In many objective exam contexts, the numerator $\pi$ and the relationship involving $2\sqrt{2}$ are often simplified.. Option D is incorrect as it represents an inverse-like structure, and other options do not follow the RMS/Average derivation. Answer: A is correct — The form factor is the ratio of the RMS value to the average value, which for a sinusoid evaluates to approximately 1.11. Exam Tip: Always remember the Form Factor of 1.11 for sinusoids and 1.15 for half-wave rectifiers; these are frequently asked in competitive exams.

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