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I am trying to calculate the current through the load resistor RL given some input voltage Vin at the top left terminal. I am also trying to find the maximum possible current through RL, and I know that R1=R4 and R2=R3.

enter image description here

I'll call the voltage at the + and - terminals of the op-amp V+ and V_ respectively. Also, I will call the voltage at the output of the op-amp Vo. Since no current will flow into the negative terminal of the op-amp, we have that the current through R1 and R4 are the same:

(Vin-V_)/R1=(V_-V0)/R4

and since R1=R4 we have Vo=2V_-Vin

Similarly, the current through R3 must sum to the current through R2 and the current through the load IL, so we have IL = I3-I2 and so

V+/RL = (Vo-V+)/R3-V+/R2

Then using the op-amp rules V+=V_ and we know R2=R3, this expression simplifies to V+ = -(RL/R3)*Vin, so the current through RL is IL = V+/RL = -Vin/R3. From here, I am unsure of what is meant by calculating the maximum current through RL. To me it seems that since the op-amp has a finite power supply, the maximum output voltage is Vo = 12volts. This would mean that the minimum input voltage is Vin = 2V_- 12volts, which leads to V+ = -(RL/R3)Vin = (RL/R3)(2V_-12volts). Rearranging leads to a maximum op-amp terminal voltage of

V+ = 12volts*RL/(2RL+R3)

and so the max current is IL = V+/RL= 12volts/(2RL+R3).

Is this analysis correct? I am not very comfortable with op-amps so I was hoping somebody could verify. One thing that is throwing me off is that the current through RL does not seem to depend on the actual resistance of the load. But on the other hand, the maximum current through RL does depend on the resistance of the load. Is somebody able to explain why this is or where I made a mistake?

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    \$\begingroup\$ HINT: Remember that op-amps strive to keep the (+) and (-) inputs at the same voltage. Thus if no input (zero volts), the (+) and (-) inputs will be at zero volts (for bipolar power supplies). \$\endgroup\$
    – user105652
    Feb 24, 2018 at 0:09

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You are right.

The calculations for the analysis of OpAmps are done assuming they are ideal. However, actual op-amps are not ideal and are limited by the Vcc supplied to them.

Take for example the gain in the following circuit -

enter image description here

Gain here is -(R2/R1).

So, Vout vs Vin should ideally be a straight line. But because the peak voltage in the circuit is limited by Vcc, the output voltage can never cross |Vcc|. Hence, Vout will saturate to Vcc.

Verify this on Falstad

This happens because the op-amps are not ideal in real life.

To answer your question, the opamp will try to behave normally as long as it does not hit the Vcc and when it does, that will give you the maximum current through RL.

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