How to Calculate Average Power Dissipation on a Resistor?

[eatsleep]

1. Given that v(t) = -6 + 12 cos(2π200t + π/4) - 9 cos(2π400t + π/6) volts. The signal is applied to a 14 kΩ resistor. Find the average power dissipated on the resistor in mW. Round your answer off to two decimal places.



2. Pavg = (sqrt(Vdc^2 + vp^2/2))/R



3. I used the above equation just P=Vrms^2/R to calculate the power, this is wrong and I'm not sure what to do.

 

[berkeman]

1. Given that v(t) = -6 + 12 cos(2π200t + π/4) - 9 cos(2π400t + π/6) volts. The signal is applied to a 14 kΩ resistor. Find the average power dissipated on the resistor in mW. Round your answer off to two decimal places.



2. Pavg = (sqrt(Vdc^2 + vp^2/2))/R



3. I used the above equation just P=Vrms^2/R to calculate the power, this is wrong and I'm not sure what to do.

What's vp? How did you combine the two cos() terms to get one AC term?

 

[eatsleep]

What's vp? How did you combine the two cos() terms to get one AC term?

I did not combine them i just added them together. vp is meant to be the the voltage peak. It would be 12 and -9.

 

[berkeman]

I did not combine them i just added them together. vp is meant to be the the voltage peak. It would be 12 and -9.

That's not correct. You need to combine the AC components to get a resultant AC waveform. What if the phases of the two AC waveforms are exactly 180 degrees apart? You will not get a very big AC waveform then.

The frequencies of the AC components are the same, so you can use Phasors to solve this question...

 

[eatsleep]

That's not correct. You need to combine the AC components to get a resultant AC waveform. What if the phases of the two AC waveforms are exactly 180 degrees apart? You will not get a very big AC waveform then.

The frequencies of the AC components are the same, so you can use Phasors to solve this question...

Is that the only way to do this question, I do not believe we have done phasors in class, also how are the frequencies the same?

 

[berkeman]

Is that the only way to do this question, I do not believe we have done phasors in class, also how are the frequencies the same?

Oh, oops, you are right. They are off by a factor of two.

 

[eatsleep]

Oh, oops, you are right. They are off by a factor of two.

I just got the right answer I used power spectrum and did Vrms^2 and added all the individual signal powers up. On the sinusoidal waveforms I divided by 2 Vrms^2/2 I am not sure why, it said that in my notes. Why did they divide by 2?

Thanks for the help