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 k²
V_n is Directly proportional to k
V_n is Directly proportional to √k
V_n is Directly proportional to k³

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.