Question

It has been given that the equation of an alternating voltage is $V=100\sqrt{2}\sin \left( 100\pi t \right)$ volt. What will be the rms value of voltage and frequency?

Answer 1

Hint: frequency can be found using the angular frequency which is the coefficient of $t$ in the voltage equation. The angular frequency will be the product of the twice of $\pi $ and the frequency. Rms voltage can be found using the peak voltage in the equation which is to be divided with the square root of $2$. This information may help you in solving this question.

Complete step by step answer:
First of all let us mention the terms given in the question. The equation of the alternating voltage is given as,
$V=100\sqrt{2}\sin \left( 100\pi t \right)$
The general equation of the alternating voltage can be shown as,
$V={{V}_{0}}\sin \left( \omega t \right)$
Where ${{V}_{0}}$ be the maximum voltage or the peak voltage and $\omega $ be the angular frequency. That is the value of angular frequency will be the coefficient of $t$. Thus we can write that,
$\omega =100\pi $
As we all know, the angular frequency is mentioned as the product of the twice of $\pi $ and the frequency. That is,
$\omega =2\pi f$
Where $f$ be the frequency. Substituting the values in the equation will give,
$\Rightarrow 2\pi f=100\pi $
The frequency can be found out using this equation which can be written as,
$\Rightarrow f=50Hz$
The rms voltage is found by the equation,
${{V}_{rms}}=\dfrac{{{V}_{0}}}{\sqrt{2}}$
From the equation of alternating voltage given in the question, we can write that,
\[\Rightarrow {{V}_{0}}=100\sqrt{2}V\]
Substituting this in the equation will give,
$\Rightarrow {{V}_{rms}}=\dfrac{100\sqrt{2}}{\sqrt{2}}=100V$

Therefore the frequency and the rms voltage are calculated as \[50Hz,100V\] respectively.

Note: The peak value is mentioned as the highest voltage that the waveform will reach. It can be compared to the highest point on a mountain. By the way the Root-Mean-Square value abbreviated as rms value is defined as the effective value of the total waveform. Normally we measure the rms value of the quantities.