(C) When the cell is in an open circuit,the balancing length $\ell$ corresponds to the electromotive force $(E)$ of the cell.$E = K\ell$,where $K$ is

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(C) When the cell is in an open circuit,the balancing length $\ell$ corresponds to the electromotive force $(E)$ of the cell.$E = K\ell$,where $K$ is the potential gradient.When the cell is connected to an external resistance $R$,the terminal voltage $V$ is measured.$V = K\ell'$,where $\ell'$ is the new balancing length.The internal resistance $r$ is given by the formula: $r = \left(\frac{E - V}{V}\right)R$.Given that $R = r$,we substitute this into the equation:$r = \left(\frac{E - V}{V}\right)r$$1 = \frac{E - V}{V}$$V = E - V$$2V = E$Substituting $E = K\ell$ and $V = K\ell'$:$2(K\ell') = K\ell$$\ell' = \ell/2$.

Class 12 Physics Current Electricity Potentiometer

Medium

In an experiment of a potentiometer for measuring the internal resistance of a primary cell,a balancing length $\ell$ is obtained on the potentiometer wire when the cell is in an open circuit. Now,the cell is short-circuited by a resistance $R$. If $R$ is equal to the internal resistance of the cell,the balancing length on the potentiometer wire will be:

AIEEE 2012 All AIEEE

A
$\ell$
B
$2\ell$
C
$\ell/2$
D
$\ell/4$

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Current Electricity

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Potentiometer

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$A$ voltmeter reads the potential difference across the terminals of an old battery as $1.2 \, V$,while a potentiometer reads $1.4 \, V$. The internal resistance of the battery is $40 \, \Omega$. What is the resistance of the voltmeter in $\Omega$?

Medium

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The $e.m.f.$ of a standard cell balances across $150 \ cm$ length of a potentiometer wire. When a resistance of $2 \ \Omega$ is connected as a shunt across the cell,the balance point is obtained at $100 \ cm$. The internal resistance of the cell is .............. $\Omega$.

Easy

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In a potentiometer arrangement,a cell gives a balancing point at $75 \, cm$ length of wire. This cell is now replaced by another cell of unknown emf. If the ratio of the emf's of two cells respectively is $3:2$,the difference in the balancing length of the potentiometer wire in above two cases will be ......... $cm$.

MediumJEE MAIN 2022

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$A$ potentiometer has a uniform potential gradient. The specific resistance (resistivity) of the material of the potentiometer wire is $10^{-7} \, \Omega \cdot m$, the current passing through it is $0.1 \, A$, and the cross-sectional area of the wire is $10^{-6} \, m^2$. The potential gradient along the potentiometer wire is:

MediumAIPMT 2001

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$A$ potentiometer is connected between $A$ and $B$ and the balance point is obtained at $203.6 \, cm$. When the end of the potentiometer connected to $B$ is shifted to $C$,then the balance point is obtained at $24.6 \, cm$. If now the potentiometer be connected between $B$ and $C$,the balance point will be at ................. $cm$.

MediumAIIMS 2010

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$A$ voltmeter reads the potential difference across the terminals of an old battery as $1.2 \, V$,while a potentiometer reads $1.4 \, V$. The internal resistance of the battery is $40 \, \Omega$. What is the resistance of the voltmeter in $\Omega$?

The $e.m.f.$ of a standard cell balances across $150 \ cm$ length of a potentiometer wire. When a resistance of $2 \ \Omega$ is connected as a shunt across the cell,the balance point is obtained at $100 \ cm$. The internal resistance of the cell is .............. $\Omega$.

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