Connecting two batteries in parallel with their positive terminals together and negative terminals together results in no change in voltage, assuming both batteries have the same voltage. This configuration maintains the same potential difference, but effectively doubles the amp-hour capacity of the combined battery system. While the voltage remains constant, the increased current capacity could allow devices connected to the batteries to draw more current without draining the batteries as quickly. However, if the batteries were connected in series (positive to negative), it would lead to a rapid drain and potential overheating of the wires. Thus, the key takeaway is that parallel connection enhances capacity without altering voltage.