> The circuit I've attached is a staightforward op-amp amplifier with a
> gain of -10.
ok

> For reasons outside the scope of this question*, I needed to add the
> resistor I've called Ra.
right

> In the traditional "virtual ground" method of analysis, Ra doesn't
> appear in the gain equation.
again correct since if the op-amp is ideal then no current will flow through
it

> I tried Ra=10k in my circuit, and indeed
> it continued to work unchanged.  But I'm pretty sure if I set Ra=0 the
> circuit would stop working!
indeed

>
> To analyze this, I guess I will need a non-ideal op-amp model.  What
> is the important parameter to include?  Finite gain?  Offset voltage?
if there was just input offset voltage the resistor would affect the DC
offset of the output but not the AC gain.

if there was just finite gain then the resistor would affect the AC gain of
the amplifier.

if you have both then it will affect both

those should be the main parameters you need to add to see the affect of the
resistor (so put them in and run the numbers) but my guess is you'd have to
make the resistor quite small for it to be noticeable.

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