Question

If \( n \) cells of emf \( E \) and internal resistance \( r \) are connected in parallel, what is the equivalent emf and internal resistance of the combination?

• A. \( E_{\text{eq}} = E \), \( r_{\text{eq}} = \frac{r}{n} \)
• B. \( E_{\text{eq}} = nE \), \( r_{\text{eq}} = \frac{r}{n} \)
• C. \( E_{\text{eq}} = E \), \( r_{\text{eq}} = nr \)
• D. \( E_{\text{eq}} = nE \), \( r_{\text{eq}} = nr \)

Hint:

For cells in parallel, the equivalent emf remains the same as one cell's emf, while the equivalent resistance decreases with the number of cells.

Answer 1

The Correct Option is A

When \( n \) cells with identical emf \( E \) and internal resistance \( r \) are connected in parallel, the equivalent emf \( E_{\text{eq}} \) remains the same as the emf of a single cell because the emf values are the same for all cells. The equivalent internal resistance \( r_{\text{eq}} \) is given by the formula for resistances in parallel: \[ \frac{1}{r_{\text{eq}}} = \frac{1}{r} + \frac{1}{r} + \cdots + \frac{1}{r} = \frac{n}{r} \] Thus, \[ r_{\text{eq}} = \frac{r}{n} \] Therefore, the equivalent emf is \( E_{\text{eq}} = E \), and the equivalent resistance is \( r_{\text{eq}} = \frac{r}{n} \).