Hint: An electrical conductor refers to a substance in which electrical charge carriers, generally electrons, can migrate readily from atom to other atom possessing the application of voltage. We can say that conductivity, in general, refers to the capability to transmit electricity or heat. On the other hand, insulators refer to the materials which hinder the free migration of electrons from one atom to another atom.
Graphite is an allotrope of carbon. In a graphite molecule, we know that one valence band electron linked to each carbon atom is free and has the capability to migrate. Therefore, graphite is a good conductor of electricity. On the other hand, in a diamond molecule, there are no free mobile electrons. Hence, there would be no flow of electrons. This is the reason which makes diamonds a bad conductor of electricity or a good insulator. Like graphite, charcoal is also an allotrope of carbon and acts as a conductor of electricity.
Graphite is denser than charcoal and has more electron availability over charcoal that can be “airy” and not as dense as graphite. It is the “less airy” environment that supplies more atom-to-atom contact and thus, less resistance. This allows greater contact over the surface area and thus more mobility for the electron flow.
This concludes that graphite (Option B) is a better conductor of electricity than charcoal (Option D) and diamond (Option A). Now, Lamp black (finely divided forms of amorphous carbon) is a fine black pigment consisting of almost pure carbon particles collected as a soot from the smoke of burning gas, oil, etc. It is commonly used in the rubber and plastic manufacturing industries. However, lamp black (Option C) does not conduct electricity.
As a result, the correct answer is Option B i.e. graphite is a good conductor of electricity.
Note: Graphite conducts electricity owing to the 'spare' electrons that have been delocalised in between the layers. Due to good conductivity, graphite is very useful as electrodes in case of electrolysis.