In a potentiometer experiment, the balancing length for a cell of emf $1.5\text{ V}$ is $60\text{ cm}$. If the cell is replaced by another cell of emf $E$, the balancing length becomes $80\text{ cm}$. The value of $E$ is

Solution

1. The principle of a potentiometer states $E=kl$, where $k$ is the potential gradient.
2. For the first cell, $1.5=k\times 60$.
3. For the second cell, $E=k\times 80$.
4. Dividing the two equations gives $$\begin{array}{rl}E/1.5& =80/60\\ & =4/3\end{array}$$.
5. Solving for $E$ yields $$\begin{array}{rl}E& =1.5\times (4/3)\\ & =2.0\text{ V}\end{array}$$.
6. Hence the answer is (B).