Two identical copper wires A and B of length 50cm are connected in parallel between the same two points of a circuit. The radius of wire A is 0.50mm and that of wire B is 1.0mm. The combined parallel arrangement carries a total current of 10A. The number density of free electrons in copper is 8.5×1028m−3, and the electron charge is 1.6×10−19C.
(a) Show that the currents in the two wires divide inversely in the ratio of their resistances and hence obtain the current in each wire.
(b) For each wire, calculate the magnitude of the drift velocity of electrons.
(c) Which of the two wires is more likely to heat up for the same duration of current flow? Justify your answer with reference to your numerical results.