What constant p.d. should be used in a potentiometer?

[andrew700andrew]

Homework Statement

I am trying to use a slide wire potentiometer and a galvanometer to find the electromotive force of an unknown cell. I have heard that the balance point at which the galvanometer needle has zero deflection should be towards the centre of the slide wire as this reduces uncertainty, however this would mean using a constant potential difference source which is twice that of the unknown cell. This would mean that the sensitivity of the instrument (in volts per centimeter) would be much higher (i.e. worse) than if the balance point was towards one end of the slide wire, meaning a lower constant p.d. source could be used and so the sensitivity would be a lower value (i.e. better). This would also decrease uncertainty in the length measurement because let's say a 1m slide wire was used and the measurement was 99 +/- 0.1cm that would give a lower percentage uncertainty than if the balance point was at 50 +/- 0.1cm . Please could someone tell me if my thinking is correct?

Homework Equations

Equation for a galvanometer:
l₁/l₂ = E₁/E₂

The Attempt at a Solution

As this is more of a discussion than a specific question I have discussed my thoughts in the first section.

Image of circuit:

 

[drvrm]

I have heard that the balance point at which the galvanometer needle has zero deflection should be towards the centre of the slide wire as this reduces uncertainty, however this would mean using a constant potential difference source which is twice that of the unknown cell. This would mean that the sensitivity of the instrument (in volts per centimeter) would be much higher (i.e. worse) than if the balance point was towards one end of the slide wire, meaning a lower constant p.d. source could be used and so the sensitivity would be a lower value (i.e. better). This would also decrease uncertainty in the length measurement because let's say a 1m slide wire was used and the measurement was 99 +/- 0.1cm that would give a lower percentage uncertainty than if the balance point was at 50 +/- 0.1cm . Please could someone tell me if my thinking is correct?

Normally in a potentiometer arrangement done with meter bridge ,we advise not to take readings towards the end to avoid the end correction
/minimize error due to joints at the end ,
moreover the random error of observation is to be minimized by taking multiple readings and finally an average.
Multiple readings are taken by varying the current through a variable resistance.
Regarding sensitivity -it is fixed by the drop of voltage per unit length of the wire and to have more sensitivity one replaces the wire of 1 meter by say a 10 meter wire .
i do not think the measurements taken at the sides(end point) will be better as the end correction will start playing a dominant role.

 

[gneill]

Adding to what drvrm said, you cannot know the total length of the wire exactly so both your l₁ and l₂ will have measurement errors associated with them. The lowest overall percentage error in those measurements will occur near the center of the wire.