A battery is connected with a potentiometer wire. The internal resistance of the battery is negligible. If the length of the potentiometer wire of the same material and radius is doubled then what happens to potential gradient?

Potential gradient or potential difference per unit length of the wire depends directly upon the following factors:
  • Current through the wire.
  • Specific resistance (resistivity) of the wire.
  • inversely proportional area of cross-section of the wire.
Now as the radius is double the area will become 4 times than the earlier value also, the specific resistance will become 1/4 times than the earlier value. But the specific resistance which is directly proportional to the area will also become 4 times and will compensate for the earlier  decrease. Thus the potential gradient will not change.

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