Question

Two cells of emf 2.0 V and 6.0 V and internal resistances 0.1 and 0.4 respectively, are connected in parallel. The equivalent emf of the combination will be:

Hint:

When cells are connected in parallel, the equivalent emf depends on the internal resistances and emfs of the cells.

Answer 1

For cells connected in parallel, the equivalent emf \( \varepsilon_{\text{eq}} \) is given by the formula: \[ \varepsilon_{\text{eq}} = \frac{r_1 \varepsilon_2 + r_2 \varepsilon_1}{r_1 + r_2}, \] where \( \varepsilon_1 \) and \( \varepsilon_2 \) are the emf values of the two cells, and \( r_1 \) and \( r_2 \) are their respective internal resistances. Substituting the given values: \[ \varepsilon_{\text{eq}} = \frac{0.1 \times 6.0 + 0.4 \times 2.0}{0.1 + 0.4} = \frac{0.6 + 0.8}{0.5} = 2.8 \, \text{V}. \] Thus, the correct answer is: \[ \boxed{(B)} \quad 2.8 \, \text{V}. \]