Discover the Formula for Calculating Potential Difference with a Potentiometer

[eil2001]

I have a homework question about a potentiometer. There is a resistor between a and b that is a uniform wire of length l, with a sliding contact c at a distance x from b. An unknown potential difference V is measured by sliding the contact until the galvonometer G reads zero. I need to show that under this condition the unknown potential difference is given by V=(x/l)E. Any ideas?

 

[npgreat]

What is meant by E?

 

[eil2001]

What is meant by E?

E is the emf.

 

[clive]

The sliding contact divides the resistor in two other resistors $$R=R_1+R_2$$ where $$R_1$$ and $$R_2$$ are proportional with corresponding lengths (x and l-x). The current is given by
$$I=\frac{E}{R}$$
and the potential difference between the ends of $$R_1$$
$$V=I\cdot R_1$$
and so on...