Determining resistances in circuits

[thereddevils]

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=11V_y

V_y=(R_y)/(R_x+R_y)

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?

 

[Mindscrape]

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.