Q109 / 125 · BITSAT 2009 · Physics

The length of a potentiometer wire is $\ell$. A cell of emf $E$ is balanced at a length $\ell / 3$ from the positive end of the wire. If the length of the wire is increased by $\ell / 2 .$ At what distance will be the same cell give a balance point.

  • A
    $2 \ell / 3$
  • Correct answer
    B
    $\ell / 2$
  • C
    $\quad \ell / 6$
  • D
    $4 \ell / 3$

Solution

Potential gradient in the first case $=\frac{\mathrm{E}_{0}}{\ell}$ $$ \therefore \quad \mathrm{E}=\left(\frac{\ell}{3}\right) \cdot\left(\frac{\mathrm{E}_{0}}{\ell}\right)=\frac{\mathrm{E}_{0}}{3} $$ Potential gradient in second case $$ =\frac{E_{0}}{3 \ell / 2} \text { (x) } \frac{2 E_{0}}{3 \ell} $$ From equations (i) and (ii), $$ \frac{\mathrm{E}_{0}}{3}-\left(\frac{2 \mathrm{E}_{0}}{3 \ell}\right) \mathrm{x} \Rightarrow \mathrm{x}=\frac{\ell}{2} $$

Hence, the correct answer is option: 'B'.

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