If points a and b are connected by a wire with negligible resistance, find the magnitude of the current in the 12.0 v battery.

V = I * R
Where V is the voltage, I is the current and R is the resistance. Using Ohm's law, you require resistance to find the current through the wire. Technically, if the wire has a resistance of 0, you will get infinite current. But this isn't possible. Maybe the negligible resistance refers to the battery's internal resistance - not the wire's resistance. 

Answer: fn = wcos50 = 38.89(9.81)(cos50) = 245.23 n