Two nonideal batteries are connected in series. Evaluate the...

When two nonideal batteries of emfs $E_1$ and $E_2$ and internal resistances $r_1$ and $r_2$ are connected in series, the equivalent internal resistance is given by $r_{eq} = r_1 + r_2$.

Since $r_1 > 0$ and $r_2 > 0$, the equivalent internal resistance $r_{eq}$ is strictly greater than both $r_1$ and $r_2$. Therefore, statement B is incorrect.

The equivalent emf of the series combination depends on the polarity of the connection. If the batteries are connected such that they aid each other, $E_{eq} = E_1 + E_2$. However, if they are connected with opposing polarities, $E_{eq} = |E_1 - E_2|$. In the opposing case, the equivalent emf is less than the larger of the two individual emfs. Therefore, statement A is not universally true and is incorrect.

Thus, both statements A and B are incorrect.