This is an inverting op-amp with closed loop gain \$A\$. The question is theoretical, so op-amp is ideal.
simulate this circuit – Schematic created using CircuitLab
I was trying to find the input impedance \$Z_i\$ of this Op-amp. Let \$i\$ be the current coming out of \$V_i\$. Then \$Z_i = \frac {V_i}{i}\$
In the first case, assuming inverting terminal is at virtual ground \$V_i -0 = R_i \times i\$
$$Z_i = \frac{V_i}{i}=R_i$$
But when I apply KVL along \$V_i – R_i- R_f- V_o\$ assuming no current is entering the OP-amp.
$$
V_i – i.R_i – i.R_f -V_o=0
$$substituting \$V_o = A.V_i\$ $$
Z_i = \frac{V_i}{i} = \frac{R_i +R_f}{1-A}
$$
Which \$Z_i\$ is correct
Best Answer
The first one is correct.
Zi = Ri
The input impedance is looking into the opamp with respect to ground. So any resistance between the input signal and ground, and since the inverting terminal is held at ground, the opamp will do everything it can to ensure that it is always held at ground.
This question has also been asked before, so its worthwhile to look through the site before posting.
Input impedance of inverting amplifier clarification