Show that, when two resistors of values and are in series, their noise model is the same as a single resistance of value . Repeat the problem for parallel resistances. Sketch the spectral density of...

Show that, when two resistors of values and are in series, their noise model is the same as a single resistance of value . Repeat the problem for parallel resistances.

Sketch the spectral density of voltage noise across a 100-pF capacitor when it is in parallel with a resistor. Make another sketch for the same capacitor but with a resistance in parallel. What can you say about the area under the curves of the two sketches?