Question

The ratio of mean value over half cycle to r.m.s value of A.C is:
$\begin{align}
  & (A)2:\pi \\
 & (B)2\sqrt{2}:\pi \\
 & (C)\sqrt{2}:\pi \\
 & (D)\sqrt{2}:1 \\
\end{align}$

Answer 1

Hint: The mean value or average value of A.C cycle over a full cycle is the average value of the entire sinusoidal waveform over one complete cycle. It is zero since both the half cycles cancel each other. The r.m.s value is the effective value of a varying voltage or current. It is equivalent to the steady D.C value which gives the same effect.

Formula Used:
${{V}_{avg}}=\dfrac{2{{V}_{peak}}}{\pi }$
${{V}_{rms}}=\dfrac{{{V}_{peak}}}{\sqrt{2}}$

Complete answer:
The mean or average value of AC waves is taken to be 0 since the negative and positive parts cancel each other and give us zero. But, if we consider half cycle of ac, we get the mean value or average value of a half cycle of ac wave as:
${{V}_{avg}}=\dfrac{2{{V}_{peak}}}{\pi }$
Where, ${{V}_{avg}}$ is the average value of voltage.
${{V}_{peak}}$ is the peak value of voltage.
The r.m.s value of an ac signal for half cycle is given as:
${{V}_{rms}}=\dfrac{{{V}_{peak}}}{\sqrt{2}}$
The ratio of mean value to rms value over half cycle of an ac is given as follows:

The ratio of mean value to rms value over half cycle of ac is $(B)\dfrac{2\sqrt{2}}{\pi }$ .

Additional Information:
Alternating current or ac is defined as the current whose magnitude and direction changes with time. The mean value of ac cycle is 0 so the rms value is considered to study the behavioral changes or trends in the current flow.

Note:
The value of mean current for half a cycle and a complete cycle are different and that must be kept in mind. The peak value, the rms value and the mean value are the 3 quantities that are usually studied to observe the behavior of ac current or voltage.