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(C) When the cell is in an open circuit,the balancing length $\ell$ corresponds to the electromotive force $(E)$ of the cell.$E = K\ell$,where $K$ is

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$\ell/2$

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(C) When the cell is in an open circuit,the balancing length $\ell$ corresponds to the electromotive force $(E)$ of the cell.$E = K\ell$,where $K$ is the potential gradient.When the cell is connected to an external resistance $R$,the terminal voltage $V$ is measured.$V = K\ell'$,where $\ell'$ is the new balancing length.The internal resistance $r$ is given by the formula: $r = \left(\frac{E - V}{V}\right)R$.Given that $R = r$,we substitute this into the equation:$r = \left(\frac{E - V}{V}\right)r$$1 = \frac{E - V}{V}$$V = E - V$$2V = E$Substituting $E = K\ell$ and $V = K\ell'$:$2(K\ell') = K\ell$$\ell' = \ell/2$.

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