What Is the Average Potential Difference in an AC Circuit?

[ttiger2k7]

[SOLVED] Average Potential Difference

Homework Statement

The voltage across the terminals of an ac power supply varies with time according to V=V_0\cos(\omega t). The voltage amplitude is V_0 = 46.0 V

From the prior question, I already figured out that the root-mean-square potential difference is 32.5. V

Question What is the average potential difference V_{{\rm a}{\rm v}} between the two terminals of the power supply?

Homework Equations

$$V_{rms}=V/\sqrt{2}$$
$$V_{rms}=Vcos(\omega*t+\varphi)$$

The Attempt at a Solution

At first I thought that the average and the rms was the same thing, but now I can't figure it out. Does it involve finding current?

 

[kamerling]

At first I thought that the average and the rms was the same thing, but now I can't figure it out. Does it involve finding current?

The average is just like the rms, except you don't square before integrating and you do not take a square root afterwards. It does noet involve finding current

 

[ttiger2k7]

Hm, I don't understand. Where would you be integrating?

 

[kamerling]

Hm, I don't understand. Where would you be integrating?

when calculating the average. How did you calculate V_rms? You integrate over one full period of the AC and divide by the length of the period.

 

[ttiger2k7]

All I did to calculate V_rms was taking V divided by square root of 2, since for any sinusoidally varying quantity the rms value is always $$\frac{1}{\sqrt{2}}$$ the value. I didn't integrate at all.