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(B) In a potentiometer, the potential gradient '$k$' is defined as $k = \frac{V}{L} = \frac{E_0 R_p}{(R_p + R_s)L}$, where '$E_0$' is the $EMF$ of the

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(B) In a potentiometer, the potential gradient '$k$' is defined as $k = \frac{V}{L} = \frac{E_0 R_p}{(R_p + R_s)L}$, where '$E_0$' is the $EMF$ of the driving source,'$R_p$' is the resistance of the potentiometer wire,'$R_s$' is the series resistance, and '$L$' is the total length of the wire.When the length '$L$' of the potentiometer wire is increased, the total resistance '$R_p$' of the wire also increases proportionally (since $R = \rho \frac{L}{A}$).If the driving source and the series resistance remain unchanged, the potential drop across the wire remains the same, but it is now distributed over a longer length.Therefore, the potential gradient '$k = \frac{V}{L}$' decreases.The balancing length '$l$' is given by the relation '$E = k \cdot l$',where '$E$' is the $EMF$ of the cell being measured.Since '$E$' is constant and '$k$' has decreased, the balancing length '$l = \frac{E}{k}$' must increase.

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

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