Question:
The balancing length for a cell is 560 cm in a potentiometer experiment. When an external resistance of 10 \( \Omega \) is connected in parallel to the cell, the balancing length changes by 60 cm. If the internal resistance of the ceil is \( {N \over {10}} \) \( \Omega \) , where N is an integer then value of N is .............
The balancing length for a cell is 560 cm in a potentiometer experiment. When an external resistance of 10 \( \Omega \) is connected in parallel to the cell, the balancing length changes by 60 cm. If the internal resistance of the ceil is \( {N \over {10}} \) \( \Omega \) , where N is an integer then value of N is .............
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With the cell open, balancing length \(l_1\propto E\); with resistance R across it, \(l_2\propto V\) where \(V=\dfrac{ER}{R+r}\). So \(r=R\left(\dfrac{l_1-l_2}{l_2}\right)\).
Updated On: Oct 31, 2026
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Correct Answer: 12
Solution and Explanation
Step 1: Open-circuit: \(l_1=560\) cm \(\propto E\). With R = 10 Ohm connected, terminal voltage drops, so \(l_2=560-60=500\) cm \(\propto V\).
Step 2: \(V=E\dfrac{R}{R+r}\Rightarrow\dfrac{l_1}{l_2}=\dfrac{R+r}{R}\Rightarrow r=R\,\dfrac{l_1-l_2}{l_2}\).
Step 3: \(r=10\times\dfrac{60}{500}=1.2\ \Omega=\dfrac{N}{10}\Omega\).
Step 4: \(N=12\).
Answer: 12
Step 2: \(V=E\dfrac{R}{R+r}\Rightarrow\dfrac{l_1}{l_2}=\dfrac{R+r}{R}\Rightarrow r=R\,\dfrac{l_1-l_2}{l_2}\).
Step 3: \(r=10\times\dfrac{60}{500}=1.2\ \Omega=\dfrac{N}{10}\Omega\).
Step 4: \(N=12\).
Answer: 12
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