- #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.

$$x( t) \ =\ 7\cos\left( 20t+\frac{\pi }{2}\right),$$

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.

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,

$$ P_{rms} \ =\ \sqrt{P_{x}},$$