Question

The form factor for a sinusoidal A.C. is:
\[\begin{align}
  & \text{A}\text{. }2\sqrt{2}\text{ }:\text{ }\pi \\
 & \text{B}\text{. }\pi :2\sqrt{2}\text{ } \\
 & \text{C}\text{. }\sqrt{2}\text{ }:\text{ 1} \\
 & \text{D}\text{. 1:}\sqrt{2}\text{ } \\
\end{align}\]

Answer 1

Hint: The formula for the form factor gives us the solution to this problem.

Formula used: The Form Factor formula is,
\[\text{Form Factor = }\dfrac{\text{RMS value}}{\text{Average value}}\]
where, RMS value = root mean square value.

Complete step by step solution:
We have to consider the rms value and the average value of a sinusoidal wave.

RMS value of a sinusoidal wave is given by,
\[{{V}_{rms}}=\dfrac{a}{\sqrt{2}}\], where a = the peak voltage of the sinusoidal wave
 And, Average value of the voltage is given by,
\[{{V}_{avg}}=\dfrac{2a}{\pi }\], where a = the peak voltage of the sinusoidal wave
\[\text{ Form Factor = }\dfrac{\text{RMS value}}{\text{Average value}}=\dfrac{\dfrac{a}{\sqrt{2}}}{\dfrac{2a}{\pi }}=\pi :2\sqrt{2}\]

Therefore, the answer is option B.

Additional information: ​The ​form factor is the ​hardware ​design​ parameter that ​defines ​and prescribes the shape, size and other components, particularly in ​electronics​.

Note: ​The smaller​form factors offer more efficient use of limited space, greater flexibility in the usage of components within a larger assembly, minimal use of material and greater ease of use and transportation. Smaller form factors have greater costs in designing, manufacturing and maintenance phases of the ​engineering lifecycle​.