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  4. In an experiment of potentiometer for measuring the internal resistance of primary cell a balancing length ℓ 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

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Q. 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

AIEEEAIEEE 2012Current Electricity

Solution:

Balancing length $I$ will give emf of cell
$\therefore E = Kl$
Here K is potential gradient.
If the cell is short circuited by resistance 'R'
Let balancing length obtained be l' then $V= kl'$
$r = \left(\frac{E-V}{V}\right)R$
$\Rightarrow \quad V = E - V\quad\quad$ [$\because - r=R$ given]
$\Rightarrow \quad 2V=E$
or,$\quad2Kl' = Kl$