# Physics of batteries (volts vs charge)

Car batteries are usually 12 V. What is the difference between buying a car battery and hooking up a bunch of cheap household batteries in series? Both would register at 12 V. I assume that cars need much more current to start an engine then regular household things like lamps and toys. Does that mean that a car battery holds more charge within it?

If we think of a simple cell battery, where there are two electrodes and an electrolyte. One electrode eventually, through chemical reaction, becomes positive and the other becomes negative. Thus in a car battery, does that mean the electrodes (if we can reduce a car battery to a primitive cell), have more charge separated on each electrode? But if that was the case, wouldn't a greater charge separation mean that the voltage would be greater between the terminals as well?

In general, what is the relation between charge and voltage? I know the equation V = U/q, just like E = F/q (similar form, in the limit that the test charge is small as to not effect the PE or electric field. V = U/q is sorta useless too, since differences matter, but nevertheless that is how we defined it). If charges are separated further, does that mean greater voltage? If more charge is separated, does that mean greater voltage?

Lastly, what is the difference b/w the charge in a 12 V car battery, and the charge in a 12 V makeshift, series strung battery from home?