CORRECTION: April 9, 2009

Typo reads (R2+R3)/(R2+R3). This typo crept into that line during the publishing process, and is not the fault of the contributor, David Tweed. If you change that term to (R2×R3)/(R2+R3), then the rest of the derivation is correct as it stands.

Answer 1—This circuit is known as a “Howland current source.” The load current is derived as follows. First, write down the equations for the voltages at the inputs of the op-amp, using superposition to account for the various voltage sources and the load current in the circuit:

 Set them equal to each other and isolate the term containing I_LOAD:

 Note that if R3/R2 = R4/R1, the following expressions are also equal:

 This makes it easy to solve for I_LOAD:

In other words, the circuit is a voltage-controlled current source. The load current is essentially independent of load voltage.

Contributor: David Tweed