So I have two questions, but they're kind of linked so I'm putting them in one.
1) I have a simple circuit with a battery connected to three lamps in series. If I then add a second battery but connect it in parallel to the first, why does the potential difference across one of the lamps and the current through all of the lamps stay the same as before? I would have thought that an extra battery should mean that more work is being done on the charges, meaning that the current should increase.
2) Why, in a parallel circuit, is the potential difference across each resistor equal to the potential difference across the battery and why do the p.d.s add to give the p.d. of the battery in a series circuit?