$\begin {array} {1 1} (A)\;\large\frac{l}{3} & \quad (B)\;\large\frac{l}{2} \\ (C)\;\large\frac{2l}{3} & \quad (D)\;\large\frac{3l}{4} \end {array}$

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The student is expected to have an understanding of the construction of a potentiometer.

Potential gradient in the first case = $ \large\frac{E_0}{l}$

$ E=\large\frac{l}{3}$ $ \large\frac{E_0}{l}$ $ \large\frac{E_0}{3}$

In the second case $= \large\frac{2E_0}{\Large\frac{3l}{2}}$

$ E = (X) \large\frac{2E_0}{\Large\frac{3l}{2}}$

On solving these two equations, we get $ x = \large\frac{l}{2}$

Ans : (B)

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