Matthiessen's rule. a. Given the resistivity values of two different scattering mechanisms (p and p), derive the expression for the total resistivity (p_total) according to Matthiessen's rule. b. A metal alloy has a resistivity of 20 0-cm due to lattice vibrations and an additional resistivity of 15 0-cm due to impurity scattering. Calculate the total resistivity of the metal alloy using Matthiessen's rule. c. You have a copper wire with a cross-sectional area (A) of 0.1 cm through which a current (1) of 2 A (amperes) is passing. The charge of an electron is approximately 1.6e- 19 C (Coulombs) and the number density of free electrons in copper is approximately 8.5e28 electrons per cubic meter. Now, calculate the drift velocity of these electrons in the copper wire due to the given current.