# NCEES Solution to Sample Question #537



## JeffC (Feb 10, 2007)

The solution for NCEES Sample Question #537 shows the formula as Erms = SQRT(k*T*R*delta f).

The formula in the EERM (Camara, 6th edition, page 42-2) is

Erms = SQRT(4*k*T*R*delta f). I do not understand why there is a difference of a factor of 4 under the square root. Can anyone explain this to me?


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## Dark Knight (Feb 10, 2007)

Jeff,

I took a look to the equations you mentioned. There is a difference. 42-2 seems to calculate the Johnson Noise voltage. I am assuming you are taking the Controls and Comm module. Problem #537 shows the formula for the rms value. I am a Power guy so I am not going to pretend I know a jack about that but there might be your difference. V 42-2 not equal to Vrms of #537. Go to 27-5 of Camara and see what the relationship is. It will be better if you see that by yourself. If we can help in any other ways. :beerchug:

For what might worth I checked in an old Comm book that I have and they use the one at Camara 42-2 all the time. I think I know what is going on, and I am editing my original post. Vrms= (V/sqrt(2)). In your problem the statement says that what you have is the Vrms. Then you have to make the modification to the formula at 42-2. Instead of 4 for the value inside you have 4/sqrt(2) Sqrt(4)/sqrt(2) is one. Don't know if I am making any sense here. It is late for me and I am tired(cannot blame it to "I am drunk") Anyways, check 27-5 and see if you can come with the same conclusion. My Comm book has a fancy explanation for that so I think it will be easier for you to do a search for "noise" and see what you can find.

Good luck in your prep.


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## benbo (Feb 13, 2007)

I remember this problem from my studying as the one from the NCEES book I just couldn't get. Johnson noise voltage, thermal noise voltage, everywhere I look they use these interchangeably. And the equation is always Erms = sqrt(4kRT(deltaf)). Luis made a valiant effort to explain it but I still don't get it. It just doesn't look like it works out to me, because they give you the RMS voltage across the resistor to start with. And they have the equation in the solutions different. Maybe another of the EE masters like singlespeed or Art could explain it to me.

I'll just say this. I never resolved this to my satisfaction, but even with this confusion I still passed the EE PE with ECC afternoon. I can't remember if we had a problem like this and I couldn't tell you even if we did.

I would just use the formula with the 4 in it, and if that doesn't seem good use the other one.


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