(A) The potential gradient $K$ of the potentiometer wire is given by:$K = \frac{V_{wire}}{L} = \frac{E_{driving} \times R}{(R + r) L}$Given $E_{drivin

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(A) The potential gradient $K$ of the potentiometer wire is given by:$K = \frac{V_{wire}}{L} = \frac{E_{driving} \times R}{(R + r) L}$Given $E_{driving} = 5 \, V$, $r = 4 \, \Omega$, $L = 5 \, m$, and $R = 16 \, \Omega$:$K = \frac{5 \times 16}{(16 + 4) \times 5} = \frac{80}{100} = 0.8 \, V/m$Case $1$: Cells assist each other $(E_{net} = E_1 + E_2)$$E_1 + E_2 = K l_1$$1.3 + 1.1 = 0.8 \times l_1$$2.4 = 0.8 \times l_1 \implies l_1 = 3 \, m$Case $2$: Cells oppose each other $(E_{net} = E_1 - E_2)$$E_1 - E_2 = K l_2$$1.3 - 1.1 = 0.8 \times l_2$$0.2 = 0.8 \times l_2 \implies l_2 = 0.25 \, m$Thus, the balancing lengths are $3 \, m$ and $0.25 \, m$.

Class 12 Physics Current Electricity Potentiometer

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$A$ potentiometer wire has a length of $5 \, m$ and a resistance of $16 \, \Omega$. The driving cell has an e.m.f. of $5 \, V$ and an internal resistance of $4 \, \Omega$. When two cells of e.m.f.s $1.3 \, V$ and $1.1 \, V$ are connected so as to assist each other and then oppose each other, the balancing lengths are respectively:

MHT CET 2023 All MHT CET

A
$3 \, m, 0.25 \, m$
B
$0.25 \, m, 3 \, m$
C
$2.5 \, m, 0.3 \, m$
D
$0.3 \, m, 2.5 \, m$

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$A$ potentiometer wire of length $100 \ cm$ and resistance $3 \ \Omega$ is connected in series with a resistance of $8 \ \Omega$ and an accumulator of $4 \ V$ whose internal resistance is $1 \ \Omega$. $A$ cell of e.m.f. $E$ is balanced by $50 \ cm$ length of the wire. The e.m.f. of the cell is: (in $V$)

MediumMHT CET 2020

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$A$ potentiometer wire $AB$ having length $L$ and resistance $12r$ is joined to a cell $D$ of $emf$ $\varepsilon$ and internal resistance $r$. $A$ cell $C$ having $emf$ $\varepsilon/2$ and internal resistance $3r$ is connected as shown in the figure. The length $AJ$ at which the galvanometer shows no deflection is

MediumJEE MAIN 2019

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For comparing the $e.m.f.$'s of two cells with a potentiometer,a standard cell is used to develop a potential gradient along the wires. Which of the following possibilities would make the experiment unsuccessful?

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In a potentiometer experiment,the null point is obtained on the $7^{\text{th}}$ wire for a given cell. To shift the null point to the $9^{\text{th}}$ wire for the same cell,what should we do?

MediumMHT CET 2022

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The length of a wire of a potentiometer is $100 \, cm$,and the $emf$ of its standard cell is $E \, volt$. It is employed to measure the $emf$ of a battery whose internal resistance is $0.5 \, \Omega$. If the balance point is obtained at $l = 30 \, cm$ from the positive end,the $emf$ of the battery is (where $i$ is the current in the potentiometer wire).

MediumAIEEE 2003

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For comparing the $e.m.f.$'s of two cells with a potentiometer,a standard cell is used to develop a potential gradient along the wires. Which of the following possibilities would make the experiment unsuccessful?

In a potentiometer experiment,the null point is obtained on the $7^{\text{th}}$ wire for a given cell. To shift the null point to the $9^{\text{th}}$ wire for the same cell,what should we do?

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