Not helped at all…………………….
You are having a laff right ? if you increase resistance anywhere in a circuit and voltage stays the same current is always going to drop (see Ohms law I = V/R if the numerator stays the same (V) and the denominator gets larger (R) the value of result (I) has to get smaller. You are making the mistake of keeping the 'wattage' at the load at eg 55watt, and sure enough to maintain 55watt at a lower voltage the current would have to increase (W-V*I) but as the voltage drops that 55watt bulb will just get dimmer, and while the number on the bulb may still say 55watt the bulb will not produce 55 watt of light because it is designed to be 55watt at 12.5 volts.
Might I suggest you're beyond help then 
If you increase the resistance in a circuit the voltage will drop. This isn't a textbook mate, the drop in voltage will cause a higher current draw.
It's 55w nominal, that's what it's rated at...... you're struggling to get this, I won't keep explaining how this all works in the real world. When you mess up the electrics on yours, let me know....I'll buy it 
It is only at pretty high frequency you get a ‘pipe’ effect with electrons where they tend to use outside of conductor, at 50Hz no probelmo ( they use solid core cable for normal domestic wiring). The reason a solid core is used in house wiring and not in machinery and vehicles is that solid cores tend to break when they are subject to movement and vibration, where stranded ‘flexibles’ do not’.
The tolerance of a resistor has nothing to do with whether it has a low or a high positive or negative coefficient of resistance, it is all down to what it is made from – when I said a standard resistor it was ‘a standard resistor that is designed (as they are) to not change resistance much as it got hotter or cooler’ (which is the opposite of a bulb filament the resistance of which changes massively as it heats up).
Actually DC has more of a tendency to arc than AC, simply because an sine wave (AC) passes through zero volts once every half cycle ( every 10mSec at 50 Hz) as it transitions from positive to negative – this will quench any arc (an arc cannot exist without voltage), DC only passes through zero volts when it is turned off, so once an arc is established there is nothing to quench it.
Again, I won't repeat what I wrote. I have a job to do 