Telephone Wire with Load and Characteristic Impedance

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SUMMARY

The discussion focuses on calculating the total resistance and characteristic impedance in a telephone wire circuit with a load impedance of 300 ohms. The user successfully determined the characteristic impedance (Z0) to be 502 - 37.4i but is confused about the total resistance in the circuit. They are attempting to reconcile the values of Z0 and the total resistance, which they initially calculated as 1000 ohms. The user seeks clarification on the relationship between the real part of the characteristic impedance and the resistance per meter, as well as how to properly set up the initial conditions for their equations.

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Now w/ Attachment: Telephone Wire w/ Load and Characteristic Impedance

Homework Statement


Please see attachment.

Homework Equations


I(z)=I+(exp(-γz)) + I-(exp(γz))
V(z)=V+(exp(-γz)) + V-(exp(γz))


The Attempt at a Solution



I solved easily for the characteristic impedance and gamma (propagation constant), but am having a little difficulty putting all of the resistances together to set up the initial conditions. This is my logic so far:

Load Impedance is 300, total resistance due to the characteristic impedance is 4*100=400, gain impedance is 400. So is the total resistance in the circuit 1000? Or do I use my value of Z0 (characteristic impedance), which I found to be 502 - 37.4i. If so, then is the total resistance of the circuit 502+300+300? I also don't understand why the real part of the characteristic impedance doesn't equal the resistance per meter times the length.

Anyhow, then I figured if the peak voltage is 110, then the peak current is Vpeak/R-total=110/1000=0.11, or some other value, whatever ends up being the correct answer from the previous paragraph, but so I can ask my questions, let's say it's 0.11. The current will decay through the line due to the propagation constant. This is where I'm pretty sure I'm making an error.
I(z)=I+(exp(-γz)) + I-(exp(γz))= = If so,

These are my conditions:

V(0)= 110= V+ + V-

I(0)=V(0)/Z-total=110/1000=0.11= I+ + I-, so 0.11= V+ /Z0 - V+/Z0,

So V+ - V- = 0.11*Z0

Then I could just solve the system of equations and plug into the original. But surely I've made some poor assumptions along the way. Can you help? Thank you!
 

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Sorry, now the problem is attached.
 

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