# Thermal noise voltage and Boltzmann's constant

## The rms value of thermal noise voltage is related to Boltzmann's constant k as

**Options: **

V_{n} is Directly proportional to k^{2}

V_{n} is Directly proportional to k

V_{n} is Directly proportional to √k

V_{n} is Directly proportional to k^{3}

Correct Answer: V_{n} is Directly proportional to √k

**Explanation:**

Noise voltage V_{n} is given by

√(4R KTB)

Where, K = 1.381×10^{-23} J/K, joules per Kelvin, the Boltzmann constant

B is the bandwidth at which the power P_{n} is delivered.

T noise temperature

R is the resistance

If K is the Boltzmann's constant, the rms value of thermal noise voltage is proportional to √k.