In this discussion, as always, much depends on what the symbol "V"
represents. There are at least five voltages of interest:
V1: The unobservable ideal noise voltage source, deep inside the
resistor, as given by the Nyquist formula.
V2: The unobservable IR drop across the ideal, noiseless, resistive
part of the resistor.
V3: The observable voltage at the terminals of the resistor.
V4: The voltage across the inductor.
V5: The voltage across the capacitor.
As mentioned previously, it is a source of endless confusion when
there are multiple ideas masquerading behind a single name.
Part of the problem can be solved by using subscripts on the symbols,
but this is like trying to sweep water uphill, because there is
always the temptation to «streamline» the notation by dropping the
subscripts. Non-experts get burned by this every time. Even for
experts who have been burned a thousand times, the temptation is
still there.
Typical computer-algebra systems do not help with this as much as
one might wish, because they will cheerfully let you redefine a
symbol. This makes all later uses of the symbol ambiguous. They
assume the user knows exactly what he's doing, which in my
experience is not a safe assumption. It would be nice to have
a system where selected symbols could be locked, so it would at
least throw a warning if it gets redefined.