Question

A cell of emf E is connected across a resistance R. The potential difference between the terminals of the cell is found to be V. The internal resistance of the cell must be –

• A. $\frac{2(E–V)V}{R}$
• B. $\frac{2(E–V)R}{E}$
• C. $\frac{(E–V)R}{V}$
• D. (E – V) R

Answer 1

Answer: (C)

$\frac{(E–V)R}{V}$

Answer 2

Terminal voltage V = E – ir

or V = E – $\left( \frac{E}{r + R} \right)$r

or V = $\left( \frac{E}{r + R} \right)$R

⇒ $\begin{matrix} \begin{aligned} & \\ & r = \left( \frac{E}{V}–1 \right)R \end{aligned} \end{matrix}$