In Iron Man 3, it shows Tony Stark having trouble charging his MK42 armour. At one point he even had a car battery connected to it. Why couldn't he use the arc reactor in his chest to charge his armour?
None of the new armors being developed used the internal power supply from Tony's internal arc reactor. All of his more recent suits (the ones he made AFTER New York) ran on their own independent power supplies. Note the fact they flew, used repulsors and fought Extremis soldiers whether Stark was in them or not.
The complex design of the Mark 42 made for some unique properties:
Each piece of independent armor had to have its own power supply to utilize the repulsor/anti-grav flight capacity.
Each piece of armor had to be able to independently and cooperatively know where it needed to be and in what order it needed to arrive to make the suit viable upon receipt. This mean they were all capable of managing their own power resources.
Each unit is capable of functioning independent of any other pieces (see Tony's unconventional one hand, one foot aerial ballet of destruction) and thus they are likely not able to be easily recharged unless the suit is in one piece.
The Mark 42 did not seem to be as physically strong as some of the other designs, possibly because of its very modular nature. Since the suit was designed to fit more than Stark, we see Pepper using it quite well, it makes sense to have the suit function without a direct link to the Arc reactor in Tony's chest.
It also makes sense to allow the suit to be recharged on ordinary electricity in the event Stark is not around (as it proved to be a useful feature). Recharging on ordinary electricity was a feature of the comic version of Iron Man from the very first designs.
His suits were designed to absorb solar energy constantly, absorb some electromagnetic energy from his enemies or to be powered directly from land-based power supplies. He could even hook his armor to land based power supplies to augment his strength briefly.
Additional References: The Iron Man Armory
First, the mk42 is a experimental armour, it's not conceived as one monolithic exoskeleton, but multiple semi-autonomous parts that assemble themselves to form the armour. Therefore, each part of the armour needs its own power source.
My hypothesis about why he doesn't use the arc reactor in his chest to charge the armour is that, as an experimental armour, there is no built-in interface with the arc reactor. So, considering its presumably complex power grid, Tony Stark don't want to directly link it to his life-sustaining device.
To add to what Thaddeus has already elaborated on: To charge the armors from his internal ARC reactor Tony need J.A.R.V.I.S. to regulate the charge. However, J.A.R.V.I.S. was malfunctioning, so it is possible that Tony did not feel comfortable putting his life in danger of the reactor failing mid charge. Plugging the suit into a conventional power source is the safer option. It also allows for Tony to remain mobile to continue his investigation in to the attacks, their source, and how to stop the situation.
My hypothesis is that the MK42 armor is designed to be controlled either remotely or by persons other than Tony himself.
In the movies, you see various scenes where the armor was controlled by Tony remotely. There was even a scene during the attack on Tony's house where Pepper was in the suit to protect her from harm. Therefore, Tony cannot presume that whoever is in the armor will have an arc reactor and designed the armor accordingly.
It may not have been designed that way, but there is no reason Tony could not have improvised on the fly and figured out a way to hook it up to his chest. It would have been much faster since the arc reactor is a far more powerful source than the other energy sources he was using (and he knows how much to power it without putting his life at risk)
It is because Tony needed the arc reactor to keep him alive. Charging his suit from his chest reactor would cause a power drain that might threaten his life.