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 .

Question

A cell, shunted by a 8 &#160; &#937; resistance, is balanced across a potentiometer wire of length 3 &#160; m . The balancing length is 2 &#160; m when the cell is shunted by 4 &#160; &#937; resistance. The value of internal resistance of the cell will be _____ &#937; .

Aicharya · Accepted Answer

Potential difference across test battery is, $∵ V = \frac{E R}{R + r} \propto l; \frac{R}{R + r} \propto l$

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

$\Rightarrow 4 (4 + r) = 3 (8 + r)$ $\Rightarrow 16 + 4 r = 24 + 3 r$ $\Rightarrow r = 8 Ω$

A cell, shunted by a 8   Ω resistance, is balanced across a potentiometer wire of length 3  …

Solution

A cell, shunted by a 8 &#160; &#937; resistance, is balanced across a potentiometer wire of length 3 &#160;…

Solution

A cell, shunted by a 8 Ω resistance, is balanced across a potentiometer wire of length 3 …