Question related to power transmission

[DarkStalker]

First of all I'd like to say hello. Secondly, my Physics is not very exceptional, so please don't mock me if I ask sth very dumb. :)

Homework Statement

A power station giving an output power of 100kW at 20000V is connected by cables to a factory.
If the resistance of the cables is 5.0 Ω, calculate:
(a) the current flowing in the cables,

Homework Equations

P=VI

The Attempt at a Solution

I tried solving this using "V=IR". Here's my attempt.

V=IR
20000 = I x 5
I = 20000/5 = 4000 A.

The actual solution given is:

Since P (Output) = IV where I is the current in the cables

I=P/V
= 100kW/20000
=...= 5A

I just need to know why we can't use "V=IR". My guess is it has to sth about a.c. or d.c.

 

[alphysicist]

Hi DarkStalker,

A more precise statement of Ohm's law would be:

$$\Delta V = I R$$

so if you want to know the current flowing from one point to another, you need the resistance between those points and the voltage difference between those points. Can you see why the 5 ohms and the 20000 V don't go together in Ohm's law in this problem?

 

[DarkStalker]

So what you're trying to say is that since we don't the potential difference between any two points on the wire, Ohm's law cannot be applied, right?
And if we knew the p.d., it would've been something like very lower than 20000?

 

[alphysicist]

So what you're trying to say is that since we don't the potential difference between any two points on the wire, Ohm's law cannot be applied, right?
And if we knew the p.d., it would've been something like very lower than 20000?

Exactly right; the 20000 V potential difference is across the cable and the factory. So, if for example, they gave you the "effective resistance" of the factory, you could combine it in series with the 5 ohms from the cable and then follow your procedure.

The solution from the book works, because it uses the total power (of cable and factory) and the total potential difference (across cable and factory).


Now that you know the current, you could actually use your approach to find what the potential difference across the cable is.

 

[BryanP]

Because the voltage is varying with the current throughout the /entire/ cable (because you have a 5 ohm resistance all the way to the factory), you cannot use ohm's law.

edit: a bit too late!

 

[DarkStalker]

Thanks a lot, all of you. :)

edit: a bit too late!

Not really. I'm so bad at physics that any different way of explaining helps.