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(B) The potential gradient $k$ of a potentiometer wire is given by $k = V/L$, where $V$ is the potential difference across the wire and $L$ is the tot

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(B) The potential gradient $k$ of a potentiometer wire is given by $k = V/L$, where $V$ is the potential difference across the wire and $L$ is the total length of the wire.When the length of the potentiometer wire is increased while keeping the driving source constant, the total resistance of the wire increases.Since the driving voltage $V$ remains constant, the current $I = V/R_{total}$ decreases.Consequently, the potential gradient $k = I \cdot \rho$ (where $\rho$ is the resistance per unit length) decreases.For a cell of electromotive force $E$, the balancing length $l$ is given by $E = k \cdot l$, or $l = E/k$.Since $k$ decreases, the balancing length $l$ must increase to balance the same electromotive force $E$.

In a potentiometer experiment, a null point is obtained at a particular point for a cell on a potentiometer wire of length $L$. If the length of the potentiometer wire is increased by a few centimeters without changing the cell or the driving source, the balancing length will:

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