# Input resistance of a circuit containing op amps

For my first problem, I am trying to find the input resistance of the circuit itself, is it just simply the input voltage V1 minus the calculated voltage at the negative terminal of the upper left op-amp divided by 1k?

For my second problem, I'm trying to construct an op-amp circuit that produces an output corresponding to this formula with one summing amplifier and one differentiating amplifier, but the input impedance seen by both V1 and V2 must be 5k:

Any tips on how to proceed? I am a bit stuck on how to force the input impedance seen by the two voltages to be 5k.

Here is what I have come up with so far for the two separate op-amps. How can I combine them while forcing both input impedances seen by V1 and V2 to be 5k?

• Your two questions are big enough to post individually. That will help readers searching the site know if the questions they see are helpful to them. Commented Apr 3, 2016 at 15:28

I am trying to find the input resistance of the circuit itself, is it just simply the input voltage V1 minus the calculated voltage at the negative terminal of the upper left op-amp divided by 1k?

Check yourself with dimensional analysis. If you divide a voltage by a resistance, do you get a resistance, or something else?

The input resistance of a circuit is how much the voltage has to change to cause a change in input current:

$$R_{\mathrm{in}}=\frac{\mathrm{d}V_{\mathrm{in}}}{\mathrm{d}I_{\mathrm{in}}}$$

If you can't figure out this value by inspection, you can calculate the input current for two different input voltages and use the differences to find the derivative (since this is a linear circuit, it doesn't matter what two points you choose).