Two batteries, E1 (emf: 3 V, internal resistance: 0.5 Ω) and E2 (emf: 6 V, internal resistance: 1.0 Ω), are connected in series by connecting the positive terminal of E2 to the negative terminal of E1. A third battery, E3 (emf: 6 V, internal resistance: 1.0 Ω), is connected in parallel with this combination by connecting its positive terminal to the positive terminal of E1 and its negative terminal to the negative terminal of E2.

What is the equivalent emf of this combination?

The equivalent emf of the combination of batteries E1, E2, and E3 remains at 9 V, as the parallel battery E3 has the same emf as the series combination of E1 and E2.

Explanation:

When calculating the equivalent emf for a combination of batteries connected in series and parallel, it is essential to consider their emfs (electromotive forces) and their internal resistances. In this scenario, we have two batteries E1 (3 V, 0.5 Ω) and E2 (6 V, 1.0 Ω) connected in series, and another battery E3 (6 V, 1.0 Ω) connected in parallel with this combination. To find the equivalent emf for the series connection, we simply add the emfs of E1 and E2 which results in a total emf of 9 V. However, when we consider the parallel connection with E3, the equivalent emf does not increase since the parallel connection does not change the total emf but only has the potential to reduce the total internal resistance.

In this particular case, we ignore any changes in internal resistance and focus on the emf. Therefore, the equivalent emf of the combination of these three batteries remains at 9 V, as the parallel battery has the same emf as the series combination (6 V from E2 is in series with 3 V from E1, adding up to a total of 9 V which is equal to the emf of E3).When two batteries are connected in series, the total emf is equal to the sum of the individual emfs. In this case, the emf of E1 is 3 V, and the emf of E2 is 6 V. So the total emf is 3 V + 6 V = 9 V.