Thermal noise power in a resistor is proportional to which quantities?

• A. The constants k, the temperature T, and the bandwidth B
• B. Only the temperature T
• C. Only the bandwidth B
• D. Only Boltzmann's constant k

Answer: (A)

Thermal noise power follows Johnson-Nyquist behavior: the noise power per unit bandwidth is kT, where k is Boltzmann's constant and T is the absolute temperature. Across a bandwidth B, the total available noise power delivered to a matched load is P = kTB. So the noise power scales with all three quantities— Boltzmann's constant, temperature, and bandwidth. Doubling the temperature doubles the noise, doubling the bandwidth doubles the noise, and k just sets the energy scale. The resistor’s value doesn’t change the available power when the load is matched, which is why all three factors appear in the expression.