Leaving Cert Electricity

Fallen Seraph

Could anyone explain this to me please? This is Q 8 from the 2002 past paper. The question reads:

The ESB supplies electrical energy at a rate of 2MW to an industrial park from a local power station, whose output voltage is 2kV. The total length of the cables is 15km.The cables have diameter 10 mm and resistivity 5x10^-8

Find:
the total resistance

the current flowing in the cables

the rate at which energy is "lost" in the cables

Finding the resistance is no problem it turns out to be 9.6 ohms but it's the current that I don't understand.

The marking scheme solution uses the formula P=IV to find the current.
But this gives a different answer to if you use the formula R=V/I which in turn gives a different answer to using the formula P=I^2xR. I don't understand why this should be.

Also my physics book (and the marking scheme) seem to treat the formulas P=IV and P=I^2xR as different formula when the second is just the first with R=V/I subbed in, could anyone explain this?

Thanks.

SOL

So,

Ohms Law: V=IR
Power: (who's?) P=I^2xR, but from ohms law, R=V/I
so P=I^2x(V/I) which =IV put in I as I =V/R and you get V^2/R which you may also see about the place. Are the answers that you are getting out by factors of 10s?


And now having done that I realise it hasn't to do with current, the current is to do with the watts. In this case you cant use V=IR cause the resistance on the circuit is presumably not just that of the wire

Watts = voltamps =IV so you get the power flowing. We know the ciruit supplys 2000kw =2kv*resistance, net result, a kiloamp. Check that is right, and good luck.

Civilian_Target

Fallen Seraph wrote:

Also my physics book (and the marking scheme) seem to treat the formulas P=IV and P=I^2xR as different formula when the second is just the first with R=V/I subbed in, could anyone explain this?

P=IV is an electrical input formula. eg. You have a kettle, it draws 9 Amps on a 220V mains, therefore it's a 2kW kettle.

P=I²R is the heat dissapation formula due to current. Current is in fact the motion of a charge through a conductor, and this manifests itself as heat as well as electrical charge. In this case, P is the power loss in the form of heat, not the applicable electrical charge you can use. If you're asked a question about loss or dissapation, this is the forumula to use.

so for part b, the current flowing is Current = Input Power / Voltage
and for part c, Dissapated power = Resistance x Current²

Fallen Seraph

Ok.. SOL seems to say that P=I^2xR and P=IV are essentially the same formula, but civilian seems to say that they are not.. Hmmm.

Is it not the case with the first that if you were to find the resistance of a circuit that had more than just a wire in it (such as an appliance) and the current that P=I^2xR would give you the power being used by the circuit? Surely P=I^2xR doesn't just give the heat formed in a wire...

Civilian_Target

OK - its a bit more complicated than that...

P in the P = IV sense is simply an expression of how much energy is used. Voltage is the pace at which the power is "pushed" into the appliance (ie. the factor that controls at what pace things can happen) while current is the push that makes it happen. That's why the Dart needs 1500V (needs a lot of push) but a lightbulb doesn't. In this case, power is just a number, usually the maximum number of joules per second that the appliance could consume. The resistance isn't necessarily relevant in this case, because it's only a maximum and not necessarily constant, although they might make you calculate it anyway.

In terms of leaving cert Physics, the only real cases when P = I²R is going to be used is heat loss in a wire, but it can pretty much be applied whenever electrical energy is converted to any other type of energy (and that's usually heat, but it could be sound in your speakers as well, for example). In this case, the power is referring to systems other than the electrical circuit, and it is simply easiest to measure the energy lost from the electrical circuit than to measure the total dissapated energy. Thanks to the law of conservation of energy, these will be equal anyway. Being able to measure the energy accurately's quite important because energy conversions with this formula also lead to the creation of entropy.

However, in the terms you're saying things you've basicly got the right idea, certainly for what you're going to need for leaving cert. P = VI is a capability formula, how many watts could this use or how much current could something draw. P = I²R refers to energy that's already been used. They are not essentially the same formula, they're quite different.

SOL

Sorry, to explain, the formula is all the same, (put it through yourself) the difference here is that in one part you need to find the power dissipated by the wire, so we only need to consider its resistance, as a piece of a circuit, in determining the current we look at all of the circuit including the place the power is going to but since we don't know the resistance of that we can't use V=IR but we have been told the power in the line and since P=IV and we know the total power... we get our answer.



to summarise, we are looking at different aspects/parts of the circuit using the same set of formulae