Why fuse needs to be slightly more able to bear current than the appliance? if I have a bulb with rated current of $4 A$ then why I need to connect an $5A$ fuse?( which has slightly more ability to bear current.)
 A: The role of a fuse is not to protect the equipment from damage. It's to ensure that in the event of a fault, the wiring doesn't overheat and cause a fire.
The fuse needs to be rated slightly higher than the maximum operating current of the protected device, so that the fuse won't blow when the equipment is used.  It shouldn't be rated too much higher than the maximum operating current, because that would require wiring the equipment with thicker, costlier wire.
In case this is a homework question, I won't talk about the specific case of the lamp directly, but give a hint in the form of a question: What is the equivalent resistance of an incandescent lamp, and how does it depend on temperature?
A: The actual amount of current that will cause a fuse with a given rating to open is a random variable that depends on random variables in the manufacturing process. Same goes for the light bulb: The actual amount of current that the light bulb will draw from a given supply voltage is variable.
In order to prevent blown fuses, you want the nominal rating of the fuse to be somewhat higher than the nominal rating of the light bulb, and in order to prevent house fires, you want the nominal capacity of the wires in the walls to be a bit higher than the rating of the fuse.
