If you double the bandwidth from 1 Hz to 2 Hz at the same temperature, what happens to the thermal noise power in the same system?

If you double the bandwidth from 1 Hz to 2 Hz at the same temperature, what happens to the thermal noise power in the same system?

• A. It doubles.
• B. It halves.
• C. It quadruples.
• D. It stays the same.

Answer: (A)

Thermal noise power in a resistor at a fixed temperature scales linearly with bandwidth. The noise is white, meaning its power per unit bandwidth is constant and given by kT, where k is Boltzmann’s constant and T is temperature. The total noise power in a bandwidth B is P = kTB. So if you double the bandwidth from 1 Hz to 2 Hz while keeping temperature the same, the total noise power doubles. For context, at room temperature kT is about 4 × 10^-21 W per Hz, so the noise in 1 Hz is ~4 × 10^-21 W and in 2 Hz it’s ~8 × 10^-21 W.

Thermal noise power in a resistor at a fixed temperature scales linearly with bandwidth. The noise is white, meaning its power per unit bandwidth is constant and given by kT, where k is Boltzmann’s constant and T is temperature. The total noise power in a bandwidth B is P = kTB. So if you double the bandwidth from 1 Hz to 2 Hz while keeping temperature the same, the total noise power doubles. For context, at room temperature kT is about 4 × 10^-21 W per Hz, so the noise in 1 Hz is ~4 × 10^-21 W and in 2 Hz it’s ~8 × 10^-21 W.