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. \(R\left[\dfrac{E}{V} - 1\right]\)
• B. \(R\left[\dfrac{E}{V} + 1\right]\)
• C. \(ER\)
• D. \((E-V)R\)

Hint:

Terminal voltage \(V = E - Ir\). Current \(I = V/R\). Substitute and solve for \(r\).

Answer 1

The Correct Option is A

Step 1: Basic Principle
Terminal voltage \(V = E - Ir\), where \(I = V/R\).
Step 2: Solution Procedure:
\[ I = \frac{V}{R}, \quad V = E - Ir \] \[ V = E - \frac{V}{R} \cdot r \Rightarrow r = \frac{(E-V)R}{V} = R\left(\frac{E}{V} - 1\right) \]
Step 3: Required Answer:
Internal resistance \(r = R\left[\dfrac{E}{V} - 1\right]\).