Q:Why in a three pin plug the earth pin is thicker and longer than the other pins?

A:It depends upon R=rho l/a where area(a) is inversely proportional to resistance (R), so if (a) increases, R decreases & if R is less the leakage current will take low resistance path so the earth pin should be thicker. It is longer because the The First to make the connection and Last to disconnnect should be earth Pin. This assures Safety for the person who uses the electrical instrument.