In an electric transmission line oflength I that carries alternating current of high

Chapter 12, Problem 8

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In an electric transmission line oflength I that carries alternating current of high frequency (called a "lossless" line), the voltage V and current i are described by 9 2 V 3 2V . LC , 0 < x < I, 0 < f, 3x2 3t2 d 2 i d 2 i = LC. 0 < x where L is the inductance per unit length and C is the capacitance per unit length. Suppose the line is 200 ft long and the constants C and L are given by C = 0.1 farads/ft and L 0.3 henries/ft. Suppose the voltage and current also satisfy V(0, t) = V(200, t) = 0, 0 < t; V(x,0) = llOsin 0 < x < 200; dV lit {x, 0) = 0, 0 < x < 200; /(0. t) /(200, t) 0, 0 < f. nx i(x, 0) = 5.5 cos , 0 < x < 200; 200 " " and 9/ dt (x, 0) = 0, 0 < x < 200. Approximate the voltage and current at; = 0.2 and t 0.5 using Algorithm 12.4 with h = \0 and k = 0.1.