Question

The voltage of a domestic ac is $220\,V$. What does this represent?
A. Mean Voltage
B. Peak Voltage
C. Root mean voltage
D. Root mean square voltage

Answer 1

Hint:In order to solve this question we need to understand AC voltage and DC voltage. So AC voltage or alternating voltage are that type of voltages which are having sinusoidal variations of voltage in circuit, it is generally used when capacitor and inductor are connected in circuit or when any wave need to propagate in space while DC voltage or direct voltage is constant voltage in time which is generally used in those circuits in which a constant current is required.

Complete step by step answer:
Since AC or alternating voltage varies sinusoidally, we cannot use that voltage because it may damage our electric equipment. Due to variation in voltage current varies and our devices could not perform well, so we require a stable voltage.

So we require average or mean voltage, but since average or mean voltage of AC is zero, we prefer root mean square voltage as a stable voltage for electrical equipment.Consider an AC voltage V varying sinusoidal as,
$V = {V_o}\sin (\omega t + \phi )$
Here, ${V_o}$ is the peak voltage.
Let the RMS voltage be defined as, ${V_{rms}}$.We know RMS is defined in terms of peak voltage as,
$\therefore {V_{rms}} = \dfrac{{{V_o}}}{{\sqrt 2 }}$

So the correct option is D.

Note:It should be remembered that we do not use peak voltage because peak voltage is achieved by AC voltage periodically and hence it may damage the other electrical equipment. We have to use average but since average is zero so we prefer to use RMS value. Actually electric transmission in our homes is done through transformers like step up and step down transformers.