In an experiment of potentiometer for measuring the internal resistance of primary cell a balancing length $\ell $ is obtained on the potentiometer wire when the cell is open circuit. Now the cell is short circuited by a resistance $R$. If $R$ is to be equal to the internal resistance of the cell the balancing length on the potentiometer wire will be
AIEEE 2012, Medium
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Balancing length $l$ will give emf of cell
$\therefore E=K l$
Here $\mathrm{K}$ is potential gradient.
If the cell is short circuited by resistance $'R'$
Let balancing length obtained be $l'$ then
${V=k l^{\prime}}$
${r=\left(\frac{E-V}{V}\right) R}$
$\Rightarrow \quad V=E-V$ $[\because r=R \text { given }]$
$\Rightarrow \quad 2 V=E$
or, $\quad 2 K l^{\prime}=K l$
$\therefore \quad r=\frac{l}{2}$
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