How Long Can Copper Wire Be in a Data Center to Limit Voltage Drop to 1V?

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Discussion Overview

The discussion revolves around calculating the maximum length of copper wire in a data center that can maintain a voltage drop of no more than 1V, given specific parameters such as power consumption and resistivity. The context includes theoretical calculations and assumptions related to electrical resistance and current draw.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant calculates the total current draw from 100,000 CPUs, each consuming 100W at 120V, resulting in a total of 83 kA.
  • Another participant notes that the length of the wire is dependent on its diameter, indicating the importance of the cross-sectional area in the calculations.
  • A participant confirms the correctness of the initial calculations regarding current draw and voltage drop equations.
  • There is a clarification regarding the variable "A," which represents the cross-sectional area of the wire, not the current in amperes.

Areas of Agreement / Disagreement

Participants generally agree on the calculations regarding current draw and the use of voltage drop equations, but there is an acknowledgment that the wire's length is contingent upon its diameter, which remains unspecified in the problem.

Contextual Notes

The discussion does not resolve the specific values for the cross-sectional area or the maximum length of the wire, as these depend on additional parameters not provided in the problem statement.

cmathis
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Homework Statement


Your data center has 100,000 CPUs. Each burns 100 W at 120 V. Copper has a resistivity of 1.7E-8 Ω*m. What is the maximum length of copper wire on the power supply to give a voltage drop of no more than 1V?


Homework Equations



P = V*I
R = (rho*L)/A, where L is the length of the wire, A is the cross-section area
V= I*R


The Attempt at a Solution



Each CPU burns 100W at 120V, therefore each draws 100W/120V = 0.83A current. 0.83A * 100,000 = 83 kA total draw. Is this right? That is a MONSTROUS amount of current.

The answer to the question would be:

V = I*R

1V = 83000A * (1.7E-8 * L)/A

L = (1V * A)/(83000A * 1.7E-8)
 
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Sorry, but the wire's length will depend on the wire's diameter.
 
I know. I left that variable as "A" in the answer (cross section area) because it wasn't given to me in the problem. The rest of the work looks fine though?
 
cmathis said:

Homework Statement


Your data center has 100,000 CPUs. Each burns 100 W at 120 V. Copper has a resistivity of 1.7E-8 Ω*m. What is the maximum length of copper wire on the power supply to give a voltage drop of no more than 1V?


Homework Equations



P = V*I
R = (rho*L)/A, where L is the length of the wire, A is the cross-section area
V= I*R


The Attempt at a Solution



Each CPU burns 100W at 120V, therefore each draws 100W/120V = 0.83A current. 0.83A * 100,000 = 83 kA total draw. Is this right? That is a MONSTROUS amount of current.
Yes, it's right!
The answer to the question would be:

V = I*R

1V = 83000A * (1.7E-8 * L)/A
L = (1V * A)/(83000A * 1.7E-8)

Good! I got confused between A = area and A = ampers there for a minute.
 

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