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(D) In a potentiometer experiment to find the internal resistance $(r)$ of a cell,the cell $E_1$ is connected in series with a resistance box $R$. Whe

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$R\left(\frac{E_1}{V}-1\right)$

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(D) In a potentiometer experiment to find the internal resistance $(r)$ of a cell,the cell $E_1$ is connected in series with a resistance box $R$. When the circuit is open,the balancing length $l_1$ is proportional to the $EMF$ $(E_1)$: $E_1 = k l_1$. When the circuit is closed (resistance $R$ is connected),the balancing length $l_2$ is proportional to the terminal potential difference $(V)$: $V = k l_2$. The internal resistance is given by the formula: $r = R \left( \frac{E_1}{V} - 1 \right)$. Here,$E_1$ is the $EMF$ of the cell,$V$ is the terminal potential difference,and $R$ is the external resistance.

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