Two cells of emf 10 V and 6 V, each having internal resistances of \( 2\,\Omega \) are connected in parallel across points A and B. The equivalent emf of the cells is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 8 V
For two cells in parallel (positive terminals joined together, as is usual for a parallel combination), the equivalent emf is
\( \displaystyle \varepsilon_{\mathrm{eq}} = \frac{\varepsilon_1 r_2 + \varepsilon_2 r_1}{r_1 + r_2} \)
\( \varepsilon_1 = 10\,\mathrm{V},\; r_1 = 2\,\Omega \)
\( \varepsilon_2 = 6\,\mathrm{V},\; r_2 = 2\,\Omega \)
\( \displaystyle \varepsilon_{\mathrm{eq}} = \frac{10 \times 2 + 6 \times 2}{2 + 2} = \frac{32}{4} = 8\,\mathrm{V} \)
Shortcut: When the two internal resistances are equal, the formula reduces to the average of the two emfs: \( (10 + 6)/2 = 8\,\mathrm{V} \).