Q:

Batteries in parallel

What will happen if 2 or more ideal batteries with different emfs are connected in parallel across a resistor?
Just curious to know what folk around here think..

A:

In ideal circuit theory, connecting two ideal constant voltage sources (batteries) in parallel (using ideal wires of course) results in a contradiction.
For example, a 1V and 2V voltage source in parallel, yields by KVL:
$$1V = 2V$$
There are many ways to draw an inconsistent circuit in ideal circuit theory so this shouldn't be particularly mysterious.
One might say that the current that circulates through the ideal voltage sources is 'infinite' thus producing a non-zero voltage across the ideal wire but that's no better, in my opinion, than saying that the circuit is inconsistent.
Of course, physical voltage sources can't produce arbitrarily large current thus, the missing circuit elements are the series ideal resistors that model the limited short-circuit current of the voltage sources and the resistance of the connecting wires.
Ideal circuit elements are used to model physical circuit elements and we must not forget to include the appropriate elements to account for the non-ideal characteristics.

A:

You'll let the magic smoke out.

