QUESTION 2 An electric cable that is not well insulated from teh ground runs along the x- -axis, such that leakage occurs along its entire length. We denote by V (x,t) and I (x, t) the voltage and the current in cable at point x and at time t. We assume that the voltage and the current satisfy the system ǝv მე ΟΙ -L - RI Ət ΟΙ მე Əv Ət GV, where L is the inductance, R is the resistance, C is the capacitance, and G is the leakage to teh graound. Show that V and I satisfy the telegraph equation a² w = LC მ2 მა + (RC + LG) + RGw. Ət² Ət
QUESTION 2 An electric cable that is not well insulated from teh ground runs along the x- -axis, such that leakage occurs along its entire length. We denote by V (x,t) and I (x, t) the voltage and the current in cable at point x and at time t. We assume that the voltage and the current satisfy the system ǝv მე ΟΙ -L - RI Ət ΟΙ მე Əv Ət GV, where L is the inductance, R is the resistance, C is the capacitance, and G is the leakage to teh graound. Show that V and I satisfy the telegraph equation a² w = LC მ2 მა + (RC + LG) + RGw. Ət² Ət
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:QUESTION 2
An electric cable that is not well insulated from teh ground runs along the x- -axis, such that leakage
occurs along its entire length. We denote by V (x,t) and I (x, t) the voltage and the current in cable
at point x and at time t. We assume that the voltage and the current satisfy the system
ǝv
მე
ΟΙ
-L - RI
Ət
ΟΙ
მე
Əv
Ət
GV,
where L is the inductance, R is the resistance, C is the capacitance, and G is the leakage to teh
graound.
Show that V and I satisfy the telegraph equation
a² w
= LC
მ2
მა
+ (RC + LG)
+ RGw.
Ət²
Ət
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