Please show work and explain thought process. If you know how to do parts but no
ID: 1767727 • Letter: P
Question
Please show work and explain thought process. If you know how to do parts but not all of whole question comment and tell me and I can ask a new questions with only the parts that you know. If you have any confusion please ask.
Consider an infinite network of resistors, each of resistance R, in a "graph paper" arrangement (see figure). The objective of this problem will be to determine the equivalent resistance between the two adjacent points A and B (imagine taking the contacts of an ohmmeter and connecting them at these points). This is not possible using the "freshman physics" method of combining resistor in series and parallel, but is possible with Fourier series techniques. First label each vertex by its "Cartesian" coordinates (m, n) where m and n are integers, so that A = (0, 0) and B = (1, 0). Show that if the voltage at each vertex is denoted by V m, n, and current I flows from the ohmmeter into A and I flow from D buck to the ohmmeter, that where delta is the Kronecker delta. With the potentials V m, n, we may construct the Fourier series of a new function where V(u, v) is bi-periodic - that is, V(u + 2pi,v) = V(u, v) and V(u, v + 2pi) = V(u, v). Find the inverse transfor-mation. i. e. find the expression for V (u, v) in terms of V(u, v). By taking the Fourier transform of both sides of (a) and carrying out appropriate simplifications, show that Now find the voltage difference VA - VB, and from that show that the effective resistance between A and B is 1/2 R. [Hint: You will get a double integral with trigonometric functions in the denominator. It will be much easier to evaluate this integral with symmetry arguments than by brute force.) Please show work and explain thought process. If you know how to do parts but not all of whole question comment and tell me and I can ask a new questions with only the parts that you know. If you have any confusion please ask.Explanation / Answer
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