I am given the circuit in the figure attached and asked to determine \(i_{o}\) as a function of \(v_{I}\). Me and a few of my colleagues have been aruging over whether the correct answer is,

\(i_{o} = \frac{-v_{I}}{R}\) or \(i_{o} = \frac{v_{I}}{R}\).

Could someone please check my analysis, I don't think I've done anything wrong.

Thanks again!

 

Looks like the famous Howland Current pump, previously discussed several times on the forum.

See page 7 of this app note.

http://www.national.com/an/AN/AN-1515.pdf

 

The analysis looks fine - all it means is that you've got the inputs reversed. The current will be positive when V1 is more positive than V2.