Calculating Resistance Given Some Knowns?

Question

Seemed simple enough, but I'm getting a really big number:

"The noise produced by a resistor is to be amplified by a noiseless amplifier having a voltage gain of 75 and a bandwidth of 100kHz. A sensitive meter at the output reads 240 uV rms. Assuming operation at 37 C, calculate the resistor's resistance."

So I used this equation: en (noise voltage) = sqrt ( 4kT * delta f*R)

Using that, I had:
240 x 10^-6 = sqrt ( 4 * 310 K * (1.38 x 10^-23 J/K)*(100 x 10^3)*R)

When I solved for R, I got an answer of 3.3661 x 10^7 ohms, which is wayyy more than the given answer of 5.985k ohms. Does anyone know what I did wrong? Thanks!

Answer 1

The resistor is the INPUT resistor

you did not refer the noise measured at the output back to the input

the noise is 3.2 uV (not the 240 uV) you used

Answer 2

the nosie voltage from the resistor is:

v = sqrt(4kT*df*R) but it goes through the amp which is noiseless and is multipled by the the gain ofthe amp, g. Thus the meter reads:

V = gv = g*sqrt(4kT*df*R)

Now solve for R: R=(V/g)^2*1/(4*k*T*df) = 5.98e3 ohms