#### Abstract

*Statistical fluctuation of electric charge* exists in all conductors, producing random variation of potential between the ends of the conductor. The effect of these fluctuations has been measured by a vacuum tube amplifier and thermocouple, and can be expressed by the formula ${\overline{I}}^{2}=\left(\frac{2kT}{\pi}\right)\int {0}^{\infty}R\left(\omega \right){\left|Y\right(\omega \left)\right|}^{2}d\omega $. $I$ is the observed current in the thermocouple, $k$ is Boltzmann's gas constant, $T$ is the absolute temperature of the conductor, $R\left(\omega \right)$ is the *real* component of impedance of the conductor, $Y\left(\omega \right)$ is the transfer impedance of the amplifier, and $\frac{\omega}{2\pi}=f$ represents frequency. *The value of Boltzmann's constant* obtained from the measurements lie near the accepted value of this constant. *The technical aspects of the disturbance* are discussed. In an amplifier having a range of 5000 cycles and the input resistance $R$ the power equivalent of the effect is $\frac{{\overline{V}}^{2}}{R}=0.8\mathrm{}\times {10}^{-16\mathrm{}}$ watt, with corresponding power for other ranges of frequency. The least contribution of *tube noise* is equivalent to that of a resistance ${R}_{c}=1.5\mathrm{}\times \frac{{10}^{5}{i}_{p}}{\mu}$, where ${i}_{p}$ is the space current in milliamperes and $\mu $ is the effective amplification of the tube.

DOI: http://dx.doi.org/10.1103/PhysRev.32.97

- Received 20 December 1927
- Published in the issue dated July 1928

© 1928 The American Physical Society