A filament of 500 Ω and its connecting wires of 0.5 Ω in all carry the same 0.4 A…

Step 1. Filament. $H = (0.4\ \text{A})^2 \times 500\ \Omega \times 1\ \text{s} = 80\ \text{J}$.

Step 2. Wires. $H = (0.4\ \text{A})^2 \times 0.5\ \Omega \times 1\ \text{s} = 0.08\ \text{J}$.

Step 3. Why. The filament's resistance is $1000$ times larger, so it makes $1000$ times the heat.