Please write the reason why each equation was used and the meanings of each letter in the equations, and explanation in written version on how to solve the problem (each section)! Thank you so much! 50 points Problem 1. Power Delivered to a Resistor Consider a cylindrical resistor with length L and cross sectional area A. The resistor is connected to a battery which maintains the voltage difference V across the resistor. Find a microscopic expression for the power delivered to a resistor in terms of the length of the resistor L, the cross sectional area of the resistor A, charge of electron e, voltage V, electron mass m, number density of electrons in the resistor n, and the mean free time . Show that your expression agrees with the formula P VI, where P is power delivered to a resistor, V is the voltage across the resistor, and I is the current flowing through the resistor You may use a different approach to answer the question, but the following steps may help you (a) Express the work done by the electric field on an electron in terms of e and V (b) Express the average speed of an electron in terms of e, m, V, L, and. (c) Express the average time Δt for an electron to cross the resistor in terms of e, m, V. L, and τ (d) Find the total work done by the electric field during the time interval Δ. (You need to figure out how many electrons pass through the resistor during Δ (e) Find the power delivered to the resistor (f) Express the current I in terms of e, n, A, and v (g) Using the average speed found in part (b), express the current I in terms of e, m, V A, L, n, and τ. (h) Show that the expression obtained in part (e) agrees with the forul P-VI 50 points Problem 1. Power Delivered to a Resistor Consider a cylindrical resistor with length L and cross sectional area A. The resistor is connected to a battery which maintains the voltage difference V across the resistor. Find a microscopic expression for the power delivered to a resistor in terms of the length of the resistor L, the cross sectional area of the resistor A, charge of electron e, voltage V, electron mass m, number density of electrons in the resistor n, and the mean free time . Show that your expression agrees with the formula P VI, where P is power delivered to a resistor, V is the voltage across the resistor, and I is the current flowing through the resistor You may use a different approach to answer the question, but the following steps may help you (a) Express the work done by the electric field on an electron in terms of e and V (b) Express the average speed of an electron in terms of e, m, V, L, and. (c) Express the average time Δt for an electron to cross the resistor in terms of e, m, V. L, and τ (d) Find the total work done by the electric field during the time interval Δ. (You need to figure out how many electrons pass through the resistor during Δ (e) Find the power delivered to the resistor (f) Express the current I in terms of e, n, A, and v (g) Using the average speed found in part (b), express the current I in terms of e, m, V A, L, n, and τ. (h) Show that the expression obtained in part (e) agrees with the forul P-VI