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  4. A cell, shunted by a 8 Ω resistance, is balanced across a potentiometer wire of length 3 m. The balancing length is 2 m when the cell is shunted by 4 Ω resistance. The value of internal resistance of the cell will be Ω.

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Q. A cell, shunted by a $8\, \Omega$ resistance, is balanced across a potentiometer wire of length $3\, m$. The balancing length is $2\, m$ when the cell is shunted by $4 \,\Omega$ resistance. The value of internal resistance of the cell will be _______$\Omega$.

JEE MainJEE Main 2022Current Electricity

Solution:

$\frac{V_{1}}{V_{2}}=\frac{3}{2}=\frac{E-i_{1} r}{E-i_{2} r}$
$=\frac{E-\frac{E}{8+r} \times r}{E-\frac{E}{4+r} \times r}$
$\frac{3}{2}=\frac{8(4+r)}{4(8+r)}$
$24+3 r=16+4 r$
$r=8\, \Omega$