Ohm's Law and AC Power: Explaining the Paradox

[waqarrashid33]

I am confuse at a point that is:
I equation P=IV there is an inverse relation between I and V But according to ohm law there is direct relation between I and V.

How in in ac Power transmission line 1100 volt cause small current than 220 volt...

please solve my this trouble...

Everyone got confused when i ask this question..

 

[willem2]

You have four variables, P, I, R and V and two relations.
P = IV
V = IR

choose the values of any two variables, and you can compute the other two.

Note that you can only combine the two relations if they both deal with the same resistance.
If you have 1100 volt and a small current, and than 220 Volt with a larger current, these voltages and currents must be across different resistances.

 

[waqarrashid33]

i mean here when we step up 220 volt then current is reduced and voltage is increased...

 

[Philip Wood]

It is generally wrong to describe P = IV as an inverse relationship between I and V. It would be right only if P were a constant.

In the 'usual' case of applying a p.d. V to a resistor of constant resistance R (i.e. the resistor obeys Ohm's law), if you double V, you will double I, and P (= IV) will go up by a factor of 4. So whatever you do to V, I will change proportionately, and P won't be constant, so P = IV doesn't give a relationship between I and V, it is simply a recipe for calculating P.

Your problem arises, I believe, because you've been required to consider how to get a given amount of power to a 'consumer'. And, using P = IV, you've thought 100 A and 10000 V would do just as well as 1000 A and 1000 V. This is true, but note that to take a current of 100 A at a p.d. of 10000 V, the consumer would have to have a resistance of 100 ohm, whereas to take a current of 1000 A at a p.d. of 1000V, the consumer would have to have a resistance of 1 ohm. So if we're considering ways of supplying the consumer with the same power at different voltages, the consumer must have different resistances in each case. That's why Ohm's law isn't applicable to the consumer in this type of calculation.

[Warning what follows is a bit compact and could cause (more?) confusion. If in doubt, I suggest you don't read it.] You might well ask: don't the end-users want a fixed voltage (110 V or 230 V or whatever)? Yes. What I've called 'the consumer' is in fact the input side of a transformer which steps the voltage down for the end users. A different transformer would have to be used if the transmission voltage going to the input of the transformer were changed. This changes the effective resistance of the consumer.