Find voltage gain and input resistance for op-amp

[ongxom]

Homework Statement

Find the input resistances and voltage gains for those ideal op amps

Homework Equations

The Attempt at a Solution

The original inverting circuit look like this :

we already have the equations :
input resistance = 10k
voltage gain = -r2/r1 = -10
For the first circuit :
it still a inverting op amps, does the red marked 10k resistor get involved with input resistances ? I think it's not because it connected to the ground (virtual ?). R2 is 100k so the equation for voltage gain remains the same as the original circuit .
Second circuit:
there is no current in red marked 10k resistor, input resistance is unchanged (10k), voltage gain remains (-10k)

I find it is difficult to calculate using op amps characteristics, can I use voltage node method to find the voltage gain, which node should I choose. Are those ground connected resistor have no effect on the circuit input resistances and voltage gain at all ?

 

[berkeman]

You are correct that because of the virtual ground property (especially with ideal opamps), the input resistances of these circuits is 10kOhms. You have a typo in the gains, however. Can you see what your typo is?

 

[ongxom]

You are correct that because of the virtual ground property (especially with ideal opamps), the input resistances of these circuits is 10kOhms. You have a typo in the gains, however. Can you see what your typo is?

Yes, for the second circuit the gain is -10.

 

[ongxom]

So can we say in those cases : In an inverting op-amp, any resistors connected to the ground can be ignored when calculate ?

 

[berkeman]

So can we say in those cases : In an inverting op-amp, any resistors connected to the ground can be ignored when calculate ?

I wouldn't say that -- it's a bit too simplified and not always true. Instead, understand what the "virtual ground" means. Can you tell us what is going on with the "virtual ground" property of a high-gain opamp with negative feedback means?