Calculating Voltage of 120V Load 750ft from Source

[enzo456]

Homework Statement

What Voltage is delivered to a 120-volt/5000-watt load which is fed with #10 AWG wire (1.24 ohms/1000') and located 750 feet from the 120-volt source?

Homework Equations

Ohm's Law E= I * R
E=(K*I*2*L)/Acmil

The Attempt at a Solution

I am in an apprenticeship program for Electrical. I was wondering if I could get some help on this problem. This is what I understand...I need to find Resistivity(K) since they do not tell me the type of wire being used. the Area in circular mils for #10 wire is 10380 circular mils. I have the length of 750 feet. I also need to find the current throughout the circuit. Since I am given the Power and Voltage of the load I calculated the Current from that:

I=P/E
I=5000w/120V
I=41.7 Amps

Now in order to find K resistivity I know that the resistance is 1.24 ohms/1000'. I understand the K is resistance per mil-foot, but this is where I come up with a problem. Any help would be appreciated...the apprenticeship program I am in is not that intense, so to work out these problems is not necessary. I am trying to learn this material because I intend to go for my bachelors degree afterwards. Thanks again

 

[Redbelly98]

Welcome to PF, enzo.

Don't worry about resistivity. What can you figure out about the wire from this information:

1. The wire is 124 ohms per 1000 ft.
2. The load is 750 feet from the source.

Extra hint: how many wires would run from the source to the load?

 

[enzo456]

i can get .00124 ohms per foot and get .93 ohms per 750 feet. if E=I*R and multiply the current of 41.7 amps and multiply that by the resistance of .93 ohms per 750 feet than I get a voltage drop of 38.8 Volts. That value doesn't seem right to me, but is that the correct way? I believe 1 wire would run from the source to the load in this problem, is that correct?

 

[Redbelly98]

You're getting there. Yes, 750 feet of wire would be 0.93 ohms.

It might help to treat the load as a simple resistor. We know that it draws 41.7A at 120V. The actual current will be different than the 41.7A number, since the voltage at the load is different than 120V.

I believe 1 wire would run from the source to the load in this problem, is that correct?

That's what many people will assume, but if you think about it just 1 wire is not enough to make a complete circuit ...

So I would draw a circuit diagram, using resistors for the load and for the wire(s) also. From there, it's Ohm's Law to figure it all out.

 

[enzo456]

so drawing it out it makes sense that there are 2 wires and the resistance for the wires 1.86 but with the load if the current is different how would I calculate the resostance for the load to treat it as a simple resistor?

 

[Redbelly98]

Good question. Since we know that it draws 41.7A at 120V, we can use Ohm's Law to figure out R for the load.

 

[trevie1970]

Yes I agree with red, find the load Resistance, you should then be able to get the voltage drop across the load R from the total resistance at 120V