Question

The same amount of current flows through the connecting wires and the bulb filament. However, it is only the filament that glows. Why?

Answer 1

The resistance of the bulb filament is very high, which means that the potential difference (voltage) across it is very high. As such, almost all of the power goes to heating the filament, which makes it give off light. In contrast, the wires have much lower resistance, so the voltage across them is also much lower, so even though the current is the same, the power used in heating the wire is tiny compared to the power used in heating the filament.