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Time Delay for DC Voltage to Appear at End of 3×10¹⁰ Meter Wire with Negligible Resistance

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  • #1 21667144
    Abdul Rawoof Shaik
    Anonymous  
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  • #2 21667145
    stephen Van Buskirk
    Anonymous  
  • #3 21667146
    Rodney Green
    Anonymous  
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  • #4 21667147
    Rodney Green
    Anonymous  
  • #5 21667148
    Earl Albin
    Anonymous  
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  • #6 21667149
    Steve Lawson
    Anonymous  
  • #7 21667150
    Abdul Rawoof Shaik
    Anonymous  
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  • #8 21667151
    Frank Bushnell
    Anonymous  
  • #9 21667152
    Steve Lawson
    Anonymous  
  • #10 21667153
    Steve Lawson
    Anonymous  
  • #11 21667154
    Frank Bushnell
    Anonymous  
  • #12 21667155
    Earl Albin
    Anonymous  
  • #13 21667156
    Steve Lawson
    Anonymous  

Topic summary

✨ The discussion addresses the time delay for a DC voltage to appear at the far end of an extremely long wire (3×10¹⁰ meters) with negligible resistance. The consensus is that the voltage propagation is governed by the speed of electromagnetic wave propagation along the conductor, not by the drift velocity of electrons. This speed is typically a fraction of the speed of light (c = 3×10⁸ m/s), often estimated between 0.5c and 0.95c depending on the wire's physical and dielectric properties. For a wire of this length, the delay ranges from approximately 100 to 200 seconds. The wire's environment and construction affect the velocity factor; for example, a spiral or coaxial cable with high dielectric constant may have a lower velocity factor (~0.1), while a straight wire in free space may approach 0.9c. Additionally, the wire's radiation resistance and capacitive effects at the open end influence signal attenuation and voltage distribution. The voltage change propagates as an electromagnetic disturbance (E/H field) along the wire, and the open end behaves like a capacitive load, forming a resonant circuit with the inductive characteristics of the wire. Practical instantaneous response is observed only over short distances; for extremely long wires, propagation delay and energy radiation become significant factors.

FAQ

TL;DR: A 3×10^10 m wire shows a voltage step after about 200 s at 0.5c; "Wires have an approximate propagation delay of 1 ns for every 6 inches." [Elektroda, Frank Bushnell, post #21667151]

Why it matters: This FAQ helps engineers, students, and hobbyists estimate real signal delays and edge‑case behaviors in ultra‑long conductors.

Quick Facts

How long until DC appears at the far end of a 3×10^10 m wire?

Treat the DC step like a fast edge. Delay ≈ distance/propagation speed. Using 0.5c gives about 200 seconds for 3×10^10 m. Faster dielectrics (e.g., VF ≈0.9) yield ≈111 seconds; very slow assumptions (0.1c) give ≈1000 seconds. [Elektroda, Frank Bushnell, post #21667151]

What is propagation delay in a wire?

Propagation delay is the time a voltage or field disturbance takes to travel along the conductor. It depends on the medium’s velocity factor, typically expressed as a fraction of light speed, not on electron drift speed. [Elektroda, Frank Bushnell, post #21667151]

What is velocity factor (VF)?

Velocity factor is the signal speed divided by light speed. Many copper structures show VF around 0.59–0.77; some environments approach 0.9, changing your delay estimate dramatically. [Elektroda, Frank Bushnell, post #21667151]

Is 0.1c a realistic speed in wire?

It’s an extreme assumption. One poster used 0.1c to illustrate a slow case, yielding ≈1000 s across 3×10^10 m. Practical cables often propagate much faster. [Elektroda, stephen Van Buskirk, post #21667145]

How do I quickly estimate wire delay?

  1. Pick an approximate velocity factor (e.g., 0.6–0.77).
  2. Compute speed: v = VF × 3×10^8 m/s.
  3. Time = distance ÷ v. A handy rule: ~1 ns per 15 cm. [Elektroda, Frank Bushnell, post #21667151]

Do electrons themselves travel that fast?

No. The energy and electromagnetic disturbance propagate near VF×c, while individual electrons drift slowly. Think fields, not particles, for timing. [Elektroda, Earl Albin, post #21667148]

What happens if the far end is open (no return path)?

An open end behaves like a capacitor. The launched step charges it, producing a voltage gradient and potential overshoot, then reflections that can ring and decay. [Elektroda, Steve Lawson, post #21667156]

Will I get the same result with a proper return path?

With a matched return path and source impedance, reflections reduce and the step settles faster. Mismatch or open ends create oscillations and slower settling. [Elektroda, Steve Lawson, post #21667156]

Can the wire radiate most of the energy?

Yes for extremely long, space‑exposed wires. Radiation resistance can dominate, so much of the launched energy radiates instead of reaching the end. [Elektroda, Rodney Green, post #21667146]

What practical rule should I remember?

“Wires have an approximate propagation delay of 1 ns for every 6 inches (15 cm) of length.” Use it for quick back‑of‑the‑envelope timing. [Elektroda, Frank Bushnell, post #21667151]

What is radiation resistance?

Radiation resistance models power lost as electromagnetic radiation from a conductor. On astronomical lengths, it can make the line look resistive. [Elektroda, Rodney Green, post #21667146]

Can the open end exceed the source voltage?

Yes. Inductive energy near the source can charge the line’s capacitance, briefly creating a higher potential at the open end before it rings down. [Elektroda, Steve Lawson, post #21667156]
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