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

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A cell, shunted by a 8Ω resistance, is balanced across a potentiometer wire of length 3m . The balancing length is 2m

Potential difference across test battery is, $∵ V = \dfrac{ER}{R + r} ∝ l; \dfrac{R}{R + r} ∝ l$

Therefore, we can write, $\dfrac{\left(\dfrac{8}{8 + r}\right)}{\left(\dfrac{4}{4 + r}\right)} = \dfrac{3}{2}$

$⇒ 4\left(4 + r\right) = 3\left(8 + r\right)$ ⇒ 16 + 4r = 24 + 3r ⇒ r = 8Ω

A cell, shunted by a 8Ω resistance, is balanced across a...

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