 #1
JamesBennettBeta
 10
 1
 Homework Statement:
 How to determine the power and RMS value of the given signals.
 Relevant Equations:

$$ P_{x} \ =\ \lim _{T\ \\rightarrow\infty } \ \frac{1}{T}\int _{T/2}^{+T/2\ } x^{2} \ ( t) \ dt,$$
$$ P_{x} \ =\ \frac{A^{2}}{2},$$
I need to calculate the power and RMS value of some equations. The problem is, I found two methods to do that and don't know which is the right method.
I have few equations to find the power and RMS value, but here is one equation.
$$x( t) \ =\ 7\cos\left( 20t+\frac{\pi }{2}\right),$$
Method #1
To find the power value,
$$ P_{x} \ =\ \lim _{T\ \rightarrow\infty } \ \frac{1}{T}\int _{T/2}^{+T/2\ } x^{2} \ ( t) \ dt ,$$
To find the RMS value,
$$ P_{rms} \ =\ \sqrt{P_{x}},$$
This seems the right method for me, but later I found a YouTube video with a completely different approach.
Methods #2
To find the power value,
$$ P_{x} \ =\ \frac{A^{2}}{2},$$
A is the amplitude of the equation.
To find the RMS value,
$$ P_{rms} \ =\ \sqrt{P_{x}},$$
I have few equations to find the power and RMS value, but here is one equation.
$$x( t) \ =\ 7\cos\left( 20t+\frac{\pi }{2}\right),$$
Method #1
To find the power value,
$$ P_{x} \ =\ \lim _{T\ \rightarrow\infty } \ \frac{1}{T}\int _{T/2}^{+T/2\ } x^{2} \ ( t) \ dt ,$$
To find the RMS value,
$$ P_{rms} \ =\ \sqrt{P_{x}},$$
This seems the right method for me, but later I found a YouTube video with a completely different approach.
Methods #2
To find the power value,
$$ P_{x} \ =\ \frac{A^{2}}{2},$$
A is the amplitude of the equation.
To find the RMS value,
$$ P_{rms} \ =\ \sqrt{P_{x}},$$