why do we perfer a 10 wire potentiometer to 4 wire potentiometer ?

@richihakunamatata has answered this question well. keep it up. 

A potentiometer consists of a long uniform wire generally made of manganin or constanton stretched on a  wooden board. A metre scale is fixed on the board parallel to the length of the wire.

The working of potentiometer is based on the fact that the fall of potential across any portion of the wire is directly proportional to the length of that portion provided the wire is of uniform area cross section  and a constant current is flowing through it.

Potentiometer is also used to measure the potential difference. It is always preferred over wheatstone bridge. Let us recollect that the wheatstone bridge has a 1 m long wire . now we know that :

V = kl where V is the potential difference to be measured , k is the potential gradient of the potentiometer and l is the length of the wire. K is constant. When l is greater , V also is greater . as a result the potential difference can be measured more accurately if the length of the potentiometer wire is more. For this reason a long potentiometer wire of 10m is preferred over a short 4m wire.

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Potential Gradient  = V / l
where V = potential gradient and l = lenght of the potentiometer wire.
To make the potentiometer sensitive , the potential gradient should be low. So by increasing the length of the wire...potential gradient reduces as it is inversely proportional and the potentiometer becomes more sensiitive.

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