Which of the following equations gives correct expression for the internal resistance of a cell by using potentiometer?

Q.1 (v) Which of the following equations gives correct expression for the internal resistance of a cell by using potentiometer?

A. \(r = R\left(\dfrac{V}{E} - 1\right)\)

B. \(r = R\left(1 - \dfrac{E}{V}\right)\)

C. \(r = R\left(1 - \dfrac{V}{E}\right)\)

D. \(r = R\left(\dfrac{E}{V} - 1\right)\)

Doubtly Asked 28 Oct 2026 Board exam · March 2025 hsc 12th Save WhatsApp Report

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Answer: D. \(r = R\left(\dfrac{E}{V} - 1\right)\)

Answer: (d) \(r = R\left(\dfrac{E}{V} - 1\right)\)

With the cell on open circuit, the balancing length \(l_1\) gives \(E \propto l_1\). When the cell is shunted by a resistance \(R\), the balancing length \(l_2\) gives the terminal p.d. \(V \propto l_2\). Since \(E = I(R + r)\) and \(V = IR\),

\[\frac{E}{V} = \frac{R + r}{R} \Rightarrow r = R\left(\frac{E}{V} - 1\right) = R\left(\frac{l_1 - l_2}{l_2}\right)\]

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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Which of the following equations gives correct expression for the internal resistance of a cell by using potentiometer?

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