Prove that the two equations of the potentiometer are equal.

Question

Can someone prove that the two equations about on wikipedia are equal.

It's the first two equations of the section called theory of operation. I don't see how R2 and RL in parrallel equal just R2*RL. Same goes for the denominator.

http://en.wikipedia.org/wiki/Potentiometer

Answer 1

They are not equal. The equation is the result of a series of operations to calculate the resistance in parallel. The equivalent resistance R1 of the parallel of R2||R3 is :

1/R1=1/R2+1/R3

If you make this substitution in both numerator and denominator, you get the resulting equation.