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The position of the balance point in a potentiometer is the point where the potential drop across the unknown resistor is equal to the potential drop across the known resistor. It depends on the current flowing through the potentiometer wire, the length of the wire, and the resistance of the wire.
(i) If the current in the potentiometer is increased, the potential gradient of the wire will also increase. This will cause the potential drop per unit length of the wire to increase, and the balance point will move closer to the cell.
(ii) If the length of the potentiometer wire is doubled, the potential drop per unit length of the wire will decrease by half. This means that the potential difference across each unit length of the wire will be half of what it was before. Therefore, the balance point will move away from the cell, as the potential drop across the known resistor will remain constant, while the potential drop across the unknown resistor will decrease due to the increased length of the wire.

Balance Point in Potentiometer
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