Question

The instantaneous voltage from an ac source is given by $E = 300\sin 314t$ what is the rms voltage of the source?

Answer 1

Hint : We find the value of the rms voltage using the formulas given below. The information given in the question is sufficient to find the solution. Initially, we find the relationship between the given equation and the standard equation for finding the voltage to find the value of input voltage. Once we find the value of input voltage, we move onto finding the value of the rms voltage by using the formula given.
The formula to find the rms voltage in a given circuit is, ${E_{rms}} = \dfrac{{{E_0}}}{{\sqrt 2 }}$
The standard value of rms voltage in a given circuit is given by, $E = {E_0}\sin \omega t$ , where ${E_0}$ is the input voltage
Value of $\sqrt 2 = 1.414$ .

Complete Step By Step Answer:
The following information is given in the question,
$E = 300\sin 314t$
Comparing this to the $E = {E_0}\sin \omega t$ , we can find the value of ${E_0}$
${E_0} = 300$ and $\omega = 314$
Now to find the value of rms voltage, we substitute the acquired values to the formula, ${E_{rms}} = \dfrac{{{E_0}}}{{\sqrt 2 }}$
After substitution we get, ${E_{rms}} = \dfrac{{{E_0}}}{{\sqrt 2 }} = \dfrac{{300}}{{\sqrt 2 }} = 212V$
In conclusion, the rms voltage for the ac source given by $E = 300\sin 314t$ will be $212V$ .

Note :
The comparison between the standard equation and the equation given in the question is to be done properly. The calculation to find the value of the rms voltage can also be found if we multiply the numerator and denominator with $\sqrt 2$ so as to make the denominator one and proceed accordingly. That will be $\dfrac{{300 \times \sqrt 2 }}{{\sqrt 2 \times \sqrt 2 }} = \dfrac{{300\sqrt 2 }}{2} = 150\sqrt 2$ . Even though we arrive at the same answer, this solution is a bit less complicated and can be understood in a quicker way.