Question

What will be r.m.s. value of given A.C> over one cycle.

A- \[\dfrac{{{V}_{0}}}{4}\]
B- \[\dfrac{{{V}_{0}}}{2}\]
C- \[\dfrac{{{V}_{0}}}{\sqrt{2}}\]
D- \[{{V}_{0}}\]

Answer 1

Hint: In this problem, we are given a sinusoidal wave of alternating current. It is clear from the given equation that they are just half waves and not the full wave.

Step by step answer:
It is clear from the figure that these waves are the output of a half wave rectifier. A half wave rectifier is a type of rectifier that only allows one half-cycle of an AC to pass, blocking the other half-cycle. Half-wave rectifiers are used to convert AC into the DC.
RMS value of voltage for a half wave rectifier: \[{{V}_{RMS}}=\dfrac{{{V}_{0}}}{2}\]

So, the correct option is (B).

Additional information:
RMS amplitude measurement is the best way to relate AC quantities to DC quantity and such measurements can be made by using oscilloscopes. the relationships between different values of current is given below:
RMS=(0.707) peak value
AVG=(0.637) peak value
The form factor of an AC is the ratio of its RMS value divided by its average value over a given period. The crest factor of an AC is the ratio of its peak to its RMS value.

Note: In an AC circuit, the current and voltage values are sinusoidal so they are constantly changing with the time. AC voltage alternates in polarity and AC alternates in direction. That is why it is known as alternating current because it changes in the path after every half cycle and the value of AC over the full cycle is zero.