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Kohlrausch Law

A cell of int...

Question

A cell of internal resistance $r$ is connected across an external resistance $n r$ . The the ratio of the terminal voltage to the emf of the cell is

\frac{1}{n}

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\frac{1}{n + 1}

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\frac{n}{n + 1}

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\frac{n - 1}{n}

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Solution

The correct option is C $\frac{n}{n + 1}$
Internal resistance $= r$ , external resistance $= n r$
Let $E =$ emf of cell.
Current drawn from cell is $I = \frac{E}{r + n r}$
If $V$ be the terminal voltage , $V = E - I r = E - \frac{E}{r + n r} r$
or $\frac{V}{E} = 1 - \frac{1}{n + 1} = \frac{n}{n + 1}$

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