ps06 - ASSIGNMENT 6 Physics 218 Due Oct 22 Fall 2004 My oce...

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ASSIGNMENT 6 Physics 218 Due Oct 22 Fall 2004 My office hours are in 114 Newman Laboratory at 1:00-3:00 PM on most Wednesdays. For meeting at other times, please send e-mail to dgc@lepp.cornell.edu to request an appointment. Appointments on Tuesdays, Thursdays, and later on Wednesdays will generally be in Wilson Lab- oratory. 1. A few useful electrical expressions in mks units are: q = Cv , v = Ldi/dt , u E = Cv 2 / 2, u M = Li 2 / 2 and the expressions for inductance L 1 and capacitance C 1 per unit length given in Prob. 3. The units of quantities in these expressions are: [ q ] = C (Coulombs), [ v ] = V (Volts), [ C ] = F (Farads), [ L ] = H (Henrys), [ i ] = A = C/s (Amps=Coulomb/second), and [ u ] = J/m 3 (Joules/meter 3 ), and [ v/i ] = Ω (Ohms). Use these and/or other simple expressions involving electrical quantities to show that the units of 1 / L 1 C 1 and 1 µ 0 ² 0 are m/s (velocity) and that the units of q L 1 /C 1 and q µ 0 0 are Ω (Ohms-resistance). L R G 1 x C 1 x 1 x 1 x 1 2. In the lecture we derived di±erential equations for electromagnetic waves on a transmission line that had resistance in the conductors as well as conductance in the insulator between the two conductors. We used the parameters L 1 , C 1 , R 1 , and G 1 for the inductance, capacitance, resistance, and conductance (per unit length) respectively. Then we found: ∂v ( x, t ) ∂x = L 1 ∂i ( x, t ) ∂t R 1 i ( x, t ) ∂i ( x, t ) ∂x = C 1 ∂v ( x, t ) ∂t G 1 v ( x, t ) (a) Show that these two equations imply the “telegrapher’s equation”: 2 v ( x, t ) ∂x 2 = L 1 C 1 2 v ( x, t ) ∂t 2 +( R 1 C 1 + G 1 L 1 ) ∂v ( x, t ) ∂t + R 1 G 1 v ( x, t ) (b) What wave equation does i ( x, t ) satisfy? (c) Assume solutions of the form v ( x, t )= V 0 e jωt + γx and i ( x, t )= I 0 e jωt + γx . Using the original equations or the equations in Parts (a) and (b), ²nd a (complex) expression for γ 2 in terms of the given parameters and ω . (Remember j = 1 in the electrical engineering convention
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This note was uploaded on 09/28/2008 for the course PHYS 218 taught by Professor Pollack during the Fall '04 term at Cornell University (Engineering School).

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ps06 - ASSIGNMENT 6 Physics 218 Due Oct 22 Fall 2004 My oce...

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