Determining resistances in circuits

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The discussion revolves around determining the maximum output voltage Vo in a circuit with a variable resistor Y and a fixed resistor X of 1 Megaohm. The maximum output voltage is suggested to be 12V, but there is confusion regarding saturation, which occurs at 15V. The relationship between the resistors is explored using the voltage divider formula, emphasizing the need for specific values of R1 and R2 for a complete solution. The conversation highlights the ideal behavior of op-amps, noting that they draw no current, which complicates the analysis with real-world resistances. Overall, the participants are working through the algebra needed to clarify the circuit's behavior at saturation.
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Homework Statement



Refer to the attachment for the diagram

(1) If the value of the variable resistor Y is varied, what is the maximum value of the output voltage Vo?

(2) If the resistance value of resistor X is 1 Megaohm, what is the resistance of the variable resistor Y immediately after saturation has occured?

Homework Equations





The Attempt at a Solution



(1) I think is 12V but i am not sure how to reason it out.

(2) At saturation, Vo=15V so 15=11Vy

Vy=(Ry)/(Rx+Ry)

I know how to carry on from here.

The answer took Vo as 12V so isn't that at saturation the output is the greater or equal to the power supply which is 15 V in this case?
 

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You can either re-derive the function of the amplifier or just look up the non-inverting amplifier.

1) You are looking for a function; that is, unless R1 and R2, or a relationship between the two, are given. You have the right formula for voltage divider, just figure out when that voltage divider, which is the input voltage to the op-amp is at a maximum.

2) The output voltage is now 15V, that's correct. Use the fact that an op-amp draws no current (ideally, though with these resistances you'd get behavior quite different from an ideal op amp). Again, without knowing R1 and R2 you will have to find the algebraic solution, which I stopped at because it looked tedious and nasty.
 

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