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Unformatted text preview: PHYS 218 - SOLUTION TO ASSIGNMENT 6 16 Mar 2007 By Chung Koo Kim e-mail : email@example.com 1. Telegraphers Equation (a) Taking the derivative of the first equation with respect to x and using the second equation gives: (subscript taken out for convenience) 2 v x 2 =- L 2 i xt- R i x =- L t- C v t- Gv- R- C v t- Gv = LC 2 v t 2 + ( RC + GL ) v t + RGv (b) Similar steps as in (a) gives identical equation, with the current taking the place of voltage: 2 i x 2 = LC 2 i t 2 + ( RC + GL ) i t + RGi (c) The trial forms of solution v ( x,t ) = V e it + x and i ( x,t ) = I e it + x , when put into either of the above two equations of motion, give 2 = LC (- 2 ) + ( RC + GL )( i ) + RG (d)-(e) As the general form we use = ( + ik ). Then from 2 = ( 2- k 2 ) + 2 ik = LC (- 2 ) + ( RC + GL )( i ) + RG we get 2- k 2 = RG- LC 2 and 2 k = ( RC + GL ) . Thus we obtain for k....
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