# Electronic – Understanding what is meant by the magnitude of an Op-Amp’s gain

circuit analysisgainoperational-amplifier

A particular problem I've been given shows two Op-Amps, which can be seen below:

I'm asked to compute the magnitude of the gain. Not being quite sure what this means, I decided I'd figure out the gain of Op-Amp (a) and then just use that as the "magnitude". Both op-amps supposedly produce an "equal" output signal – I chose A because it has no missing values

### Computing the gain

Op-Amp (a) just looks like a simple op-amp to me. I can derive gain as follows:

1. $$\I_{feedback} = \frac{V_{out} – V_{in}}{10000}\$$
2. $$\I_{input} = -I_{feedback} = -\frac{V_{out} – V_{in}}{10000}\$$
3. $$\\frac{V_{out} – V_{in}}{10000} = -\frac{V_{out} – V_{in}}{10000}\$$, $$\V_{out} – V_{in} = -V_{out} + V_{in}\$$, $$\2V_{out} – 2V_{in}\$$, $$\2V_{out} = 2V_{in}\$$, $$\\frac{V_{out}}{V_{in}} = 1\$$

# Magnitude of the gain

Here is where I find myself stuck. The gain isn't apparently the magnitude, and the correct answer has units Ohms. What could magnitude mean in this respect?

Why is this the case? Is their some special meaning to magnitude in this respect?

### Edit

I'm adding a sensor mentioned before which may have been needed (I didn't think it was relevant to the question originally)