In a potentiometer circuit, a cell of emf $E$ is balanced by a length $l$ of the potentiometer wire. If the internal resistance of the cell is $r$ and it is shunted by a resistance $R$, the balancing length becomes $l^{\prime }$. What is the internal resistance $r$ in terms of $E$, $l$, $l^{\prime }$, and $R$?

1. A.$r=R\left(\frac{l-l^{\prime }}{l^{\prime }}\right)$
2. B.$r=R\left(\frac{l^{\prime }-l}{l}\right)$
3. C.$r=R\left(\frac{l-l^{\prime }}{l}\right)$
4. D.$r=R\left(\frac{l}{l-l^{\prime }}\right)$