Determine the position of the slider on the pot

[gneill]

I just can't get in my thick skull...

Refer to the diagram in post #4.

 

[Harrison01]

What happened to the equation you spent so much time deriving? x should be a unitless number, representing the fraction of the potentiometer that is Ra.

Ok i understand that x and (x-1) are unitles numbers as we yet don't know their value but we do know that their value sums up to 10kohms. We therefore need to work out the ratio. We know we have a Vout of 3v and that Rl is 5kohms. I just can't seem to understand how we use all this data to give us the value of Ra or Rb which will then give us the opposing figure.

 

[gneill]

Ra is x*R. Rb is (1-x)R. R is the value of the potentiometer, 10000 Ohms.

Ra + Rb = R

x*R + (1-x)*R = R

x is just a value that "cuts" the potentiometer into two pieces. The two pieces sum to the whole.

 

[braceman]

I haven't touched anything like this in years and was following this through ok till i hit post 21 and 22.

Could someone please explain how we specifically get the (Rb*Rl)+(Ra*Rl)+(Rb*Ra) part of Vout= E* Ra*Rl/[(Rb*Rl)+(Ra*Rl)+(Rb*Ra)]

I just can't see why its Rb X Rl + the rest..

Could someone show or explain how these 3 are derived.
I would be very grateful.

 

[gneill]

I haven't touched anything like this in years and was following this through ok till i hit post 21 and 22.

Could someone please explain how we specifically get the (Rb*Rl)+(Ra*Rl)+(Rb*Ra) part of Vout= E* Ra*Rl/[(Rb*Rl)+(Ra*Rl)+(Rb*Ra)]

I just can't see why its Rb X Rl + the rest..

Could someone show or explain how these 3 are derived.
I would be very grateful.

Expand the expression for the output of the voltage divider using the given components.