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I recently read that in order to conduct electricity over vast distances via power lines they had to step up voltage which results in a decrease in current through the medium. This is reflected in the formula $P=IV$. What I can’t seem to grasp is why this results in current ($I$) dropping and not rather power ($P$) increasing? I’m assuming they have to somehow keep the power constant, preventing it from increasing in some way, but how is this achieved? Please excuse the silly question as I am still very new to the subject, but I just assumed from the formula above that increase in $V$ would naturally result in an increase in $P$? Is there something I am missing? :|

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  • $\begingroup$ Relevant en.wikipedia.org/wiki/… $\endgroup$ – innisfree May 30 '20 at 21:07
  • $\begingroup$ Thanks so much guys! After reading all your posts, it has finally clicked. I think what opened the door to understanding for me was that I wasn't considering the fact that, once generated, power remains a constant as you cannot create more energy out of thin air (conservation of energy). Yes, power can change but only at source during generation process, but once on the line it's V and I that represent 2 variable sides of the same coin, that of a finite amount of electrical energy that has been generated. @Harish Chandra Rajpoot, thanks for pointing out the previous post to me. $\endgroup$ – Trevor Langeveldt Jun 1 '20 at 6:41
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I think its a wording problem rather than a lack of physics knowledge in regards to efficiency and power etc. When we say we're altering a single quantity, we must keep the other the same and then determine the effects on the final:

for example, $V$ is increased, $I$ is kept the same, what happens to $P$? It increases. $V$ is kept constant, $I$ is increased then $P$ increases. See?

For this scenario, $P$ is what is kept constant, because $P$ comes in many forms, not just in terms of current and voltage. It's what is generated at the power station from chemical and kinetic energy etc converted into electrical. So $P$ is kept constant because that is what we are generating, irrelevant to the choice of $I$ and $V$ we transfer that power at.

$I$ and $V$ are then chosen from that set $P$ quantity, and for highest efficiency, like the other answers say, greater $V$ is more efficient; $V$ increases so for constant $P$, $I$ must decrease. Big $I$ creates a lot of heat.

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    $\begingroup$ Thanks so much for your insight @SamuraiMelon. It makes a lot more sense to me now! You cannot create more power/energy out of thin air, duh i feel so stupid now. But it's still a great feeling to be able to finally connect the dots! $\endgroup$ – Trevor Langeveldt Jun 1 '20 at 6:23
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What I can’t seem to grasp is why this results in current (I) dropping and not rather power (P) increasing?

When we say that increasing the transmission decreases the current, we're considering the case where we're (for example) designing a power transmission system and we have a certain group of customers to serve. For example, a certain number of residences with a certain number of light bulbs and microwave ovens and air conditioners and so on.

The power required by these customers is assumed to be constant, and whatever voltage we choose for the transmission line, we'll convert it to the local mains voltage (120 or 240 V, typically), using a transformer, before delivering it to the customers.

So we'll change the design of the transformers we use to connect the generator to the transmission line, and the transmission line to the end customers, to produce the voltage we want on the transmission line.

That means the power required by the customers stays constant, and however we change the transmission line voltage, the current required varies inversely.

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Notice, if other losses are neglected then the electric power $P$ remains constant depending on the supply source (like electric generator). Power $P=VI$ is the product of two variables i.e. voltage $V$ & electric current $I$ through the conductor (assuming power factor $1$).

Therefore if the voltage $V$ increases, electric current $I$ through the conductor decreases and vice versa to keep the power $P=VI$ constant.

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Ignoring all the heat losses, power being constant is just a statement of the conservation of energy!

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The issue in power transmission is to do it efficiently (at low cost) and safely.

The power requirement is fixed. It is basically the voltage times current (forgetting power factor for the moment). The higher the transmission voltage, the lower the current for the same power. The lower the current, the smaller the wire size. The smaller the wire size, the lower the cost of the conductor material (copper, aluminum, etc.).

The down side is shock hazards at high voltage. That requires the primary high voltage transmission lines to be elevated well off the ground to reduce the likelihood of contact with high voltage lines. That adds cost to installation. But overall, it is more cost efficient to transmit ac power at high voltage and low current.

Hope this helps.

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  • $\begingroup$ Bob D, you do mention wire size but I don't see why the wire size can be smaller with a lower current. What is the reason the wire size can be smaller if the current is lower? $\endgroup$ – Alfred Centauri May 30 '20 at 23:46
  • $\begingroup$ Because power losses in transmission vary as square of current but only linearly with resistance. $\endgroup$ – Bob D May 31 '20 at 6:35
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What is the source of this power? Maybe a hydroelectric power plant or a nuclear one or anything. So this generated some power, correct? Now ask yourself this. If you used a transformer (which when oversimplified is just two unpowered coils) at the output of this plant, would the energy or power change?

Spoiler Alert: No, it would not. There is no reason why it would change. Now, as you said, if the voltage increases, there is only one parameter that could change, which is the current.

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Yes, there is something you are missing, and it is a device called a transformer.

To minimize power losses in a given transmission line, which scale as (current squared) x (resistance in the line), one must minimize current. A device called a transformer boosts the voltage while cutting current in the same proportion. So we position a step-up transformer at the source end of the line, which increases voltage and decreases current, and then we position a step-down transformer at the load end of the line, which reduces the voltage to manageable and safe levels and boosts current.

At every step of the process, the product (voltage) x (current) which equals power remains the same, except for small losses in the transformers involved.

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