If the length of the potentiometer wire is increased by keeping constant potential difference across the wire, then

Step-by-step solution

The potential gradient k represents the potential drop per unit length and is defined by k = V / L where V is the potential difference across the potentiometer wire and L is the total wire length. Since V remains constant while L increases, the potential gradient k must decrease, making option B incorrect. For an unknown electromotive force E balanced by the potentiometer, the null point occurs at length l satisfying E = k l . Substituting the expression for k yields E = (V / L) l , which rearranges to l = E (L / V