# Copper Wire Voltage Drop

1. May 27, 2013

### cmathis

1. The problem statement, all variables and given/known data
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?

2. Relevant 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

3. 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)

2. May 27, 2013

### rude man

Sorry, but the wire's length will depend on the wire's diameter.

3. May 27, 2013

### cmathis

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?

4. May 27, 2013

### rude man

Yes, it's right!
Good! I got confused between A = area and A = ampers there for a minute.