A fused bulb does not light up due to a break in the filament. The filament is a thin wire inside the bulb that gets heated up when an electric current passes through it, producing light. When the filament breaks, the circuit is interrupted, and the bulb cannot light up.

Here is a detailed explanation of why a fused bulb does not light up:

1. Filament in the bulb:
- The filament is a crucial component of an incandescent bulb that produces light when it gets heated up.
- It is usually made of tungsten, which has a high melting point and can withstand the heat generated by the electric current passing through it.

2. Break in the filament:
- Over time, due to repeated heating and cooling, the filament may weaken and eventually break.
- This can happen if the bulb experiences a sudden jolt or if it is subjected to excessive voltage.
- A break in the filament causes an open circuit, preventing the flow of electric current.

3. Open circuit and lack of current flow:
- When the filament breaks, the circuit is interrupted, and the bulb cannot light up.
- An open circuit means there is a gap or break in the path for the electric current to flow.
- Without a complete circuit, the electric current cannot reach the filament and heat it up to produce light.

4. Testing a fused bulb:
- To confirm if a bulb is fused, one can visually inspect the filament.
- In a fused bulb, the filament will appear broken or disconnected.
- Another way to check is by using a multimeter, which can measure the continuity of the filament.
- If the multimeter shows no continuity, it indicates a break in the filament.

In conclusion, a fused bulb does not light up because of a break in the filament. The filament, which is responsible for producing light when heated, may weaken and eventually break due to factors like excessive voltage or sudden jolts. The break in the filament creates an open circuit, preventing the flow of electric current and resulting in the bulb's failure to light up.