Verify that the thermal noise PSD given by Eq. (8.23) does indeed have units of V²/Hz.
V_{R}^{2}(f)=4 k T R\ \mathrm{with~units~of~V^{2}/H z} (8.23)
The term kT has units of Joules (or Watt-sec) and can be thought of as thermal energy. The units for Joules can be written as
kT, units = Joules = Watt·sec = volts·amps·sec = volts·columbs
knowing amps = columbs/sec. The units of resistance, R, can be written as
R, units of Ω = \frac{\text{volts}}{\text{amps}} = \frac{\text{volts}}{\text{columbs/sec}} = \frac{\text{volts}}{\text{columbs}\ \cdot \ \text {Hz}}
The units for thermal noise PSD, 4kTR, are then V²/Hz.