# Telephone Wire with Load and Characteristic Impedance

In summary, the conversation involves solving for the characteristic impedance and propagation constant in a circuit with a load impedance of 300 and a total resistance of 1000. The person is unsure if the total resistance should be 1000 or 502+300+300, and also has questions about the decay of current through the line. They have set up initial conditions and equations, but are unsure if their assumptions are correct and are seeking assistance.
Now w/ Attachment: Telephone Wire w/ Load and Characteristic Impedance

## 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!

#### Attachments

• physics.jpg
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Last edited:
Sorry, now the problem is attached.

## 1. What is telephone wire with load and characteristic impedance?

Telephone wire with load and characteristic impedance refers to the electrical properties of the wire used in a telephone system, including its resistance and capacitance. These properties affect the transmission of signals through the wire and can impact the quality of the telephone call.

## 2. How does the load affect the performance of telephone wire?

The load, or the devices connected to the telephone wire, can affect the performance of the wire by altering the impedance of the system. This can result in signal distortion or loss, leading to poor call quality.

## 3. What is characteristic impedance and why is it important in telephone wire?

Characteristic impedance is the measure of the wire's opposition to an electrical current. In telephone wire, it is important because it determines the amount of signal that can be transmitted through the wire without distortion or loss. A mismatch in characteristic impedance can lead to poor call quality.

## 4. How is characteristic impedance measured in telephone wire?

Characteristic impedance is typically measured in ohms using specialized equipment or by calculating the ratio of voltage to current. The standard characteristic impedance for telephone wire is 600 ohms.

## 5. What factors can affect the characteristic impedance of telephone wire?

The characteristic impedance of telephone wire can be affected by various factors, including the type and length of the wire, the number and types of devices connected to it, and any damage or interference in the wire. It is important to properly install and maintain telephone wire to ensure the correct characteristic impedance for optimal performance.

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