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In a potentiometer arrangement, a cell of emf $1.25 \mathrm{~V}$ gives a balance point at $35.0 \mathrm{~cm}$ length of the wire. If the cell is replaced by another cell and the balance point shifts to $63.0 \mathrm{~cm}$. what is the emf of the second cell?
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Given, $\ell_1=35 \mathrm{~cm}, \ell_2=63 \mathrm{~cm}$,
$$
\mathrm{E}_1=1.25 \mathrm{~V}, \mathrm{E}_2=?
$$
By relation, $\frac{\mathrm{E}_2}{\mathrm{E}_1}=\frac{\ell_2}{\ell_1}$
or $\mathrm{E}_2=\mathrm{E}_1 \frac{\ell_2}{\ell_1}=1.25 \times \frac{63}{35}=2.25 \mathrm{~V}$
$$
\mathrm{E}_1=1.25 \mathrm{~V}, \mathrm{E}_2=?
$$
By relation, $\frac{\mathrm{E}_2}{\mathrm{E}_1}=\frac{\ell_2}{\ell_1}$
or $\mathrm{E}_2=\mathrm{E}_1 \frac{\ell_2}{\ell_1}=1.25 \times \frac{63}{35}=2.25 \mathrm{~V}$
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