How do I calculate Vo/Vs for a potentiometer circuit with varying resistance?

[tanky322]

Homework Statement

In the circuit below, the wiper divides the potentiometer resistance between $$\alpha R$$ and$$\ (1- alpha R)$$, 0 $$\leq$$$$\alpha$$ $$\geq 1$$. Find Vo / Vs

Homework Equations

KVL
KCL

The Attempt at a Solution

Im thinking that the Pot. Resistance will be R +(1-$$\alpha$$)R. Then to find the voltage (R +(1-$$\alpha$$)R)I

 

[mgb_phys]

You can ignore the resistance of the main part of the pot to ground that is below the wiper because it is in parallel with a short circuit.
The resitance of the pot is simply, R - alphaR = R(1-alpha)

 

[tanky322]

So would the answer be:

(($$\Sigma$$R)/I)Vs


Sorry about the formatting, I need to learn how to use the system.


Thanks


Andrew