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## 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 ?