You would do better not talking about 'broadswords' or 'longswords'. In effect most of the swords used in the series would be (roughly) comparable to Type X from Oakeshott's typology. These fit the single hand grip, fuller running nearly full length of the blade, little tapering a slightly rounded at the tip. These are effectively cutting blades as armour of the period in the show is not sufficient to protect the user. The Longsword is historically a later invention with a far more tapered profile and stiffer blade to be used for thrusting through the gaps in plate armour. I wouldn't call any of the blades in Merlin a longsword as it doesn't really fit the level of technology of the 'fantasy' historical time.
Another point is that the height or strength of the wielder doesn't really matter when talking of the length of the sword (unless it's a child or dwarf I suppose). Granted if your thinking of the huge 50" Scottish claymores or the greatswords used by German landesknecht (also popular in Denmark) in the 16th century it might, but otherwise it is more about the balance than weight. A 2lb sword can be harder to wield than a 40"+ 4lb sword if the balance is off. A well balanced longer sword will not feel heavy to use and there are single handed techniques for using 2-handed swords to prove it.
See the following link for a sample of Oakeshott's work on classifying swords of the medieval period.