What is the wavelength of the potential wave on this

Question

Asasignment

1) A lossless transmission line is connected to a generator of V_g = 10 cos (10000t) . The internal impedance of the generator is 50+j150 ohms. The characteristic impedance of this transmission line is 50 ohms and a load of j100 ohms is at the end of the line. The length of the line is 10m and β =0.0785 rad/m. (tan 0.785 = ˜l.)

a) What is the input impedance at the generator end on this transmission tine?

b) What is the input voltage to the transmission line? (Write 2 expressions for the input voltage)

c) What is the reflection coefficient of this tine?

d) How far this voltage wave should travel to experience a phase shift of 240°?

e) What is the wavelength of the potential wave on this transmission line?

g) What is the standing wave ratio (S) for this transmission line?

h) What will be the input impedance of this line if it is short circuited?

i) Think about the transmission line parameters R,G,L,C and fill in the blanks either by conductor/ insulator part of the transmission line.

R: is the resistance due to the ________
G: is the conductance due to the ________
C: is the capacitance due to the ________
L: is the inductance due to the ________

2) The time domain expression of a total voltage at a transmission line is as following:

v(z, t) = 200 e^0.0002z cos(1000t + 0.25 z - 30°) + 180 e^-0.0002z cos(1000t - 0.25z - 30°) (z is the distance from the load)
Characteristic impedance of TL line is Z_o = 100 Ω

a) List the following for this transmission line:

Attenuation constant (α), phase shift constant (β), incident wave voltage (V_e⁺), reflection coefficient (Γ).

b) How far this wave should travel for an attenuation of 10 %.

3) There is vector field of M = <10, -20x, 30y > present in a medium. The surface facing this vector field is located on xy-plane with 0 < x < 10, 0 < y < 20. Calculate the flux due to this vector field on this surface.

4) There is force field of F =< 50, -30x, 40> present in a medium. An object is moving due to force field F form point P:(0,1,2) to point Q:(0,2,4). Calculate the work done by the force field as a result of this displacement.