# Electronic – Does a battery powered resistor have Johnson Noise

noise

The mean noise voltage for Johnson (Thermal) Noise is given by the formula:

$$\ v_n = \sqrt{4kTR\Delta{f}} \$$.

The bigger the resistance of a resistor or the higher the frequency of a voltage supply, the higher the thermal noise the resistor will have. Does the formula also indicate if the voltage is supplied by a battery (DC, or a voltage of 0Hz frequency), any noise you measured on the resistor cannot be due to thermal noise because:

$$\ v_n = \sqrt{4kTR \cdot 0} = 0V \$$ ?

The question should be – what is $$\ \Delta f? \$$