I was reading about power transmission on wikipedia and came across the explanation of the efficiency of AC power transmission that said power in the load = (I^2)* R while power transmitted= IV. The page then says "Thus, the same amount of power can be transmitted with a lower current by increasing the voltage." What I don't understand is how voltage can be increased without also increasing current, this seems to violate ohm's law. How is this possible?


The AC voltage is stepped up or down using transformers, and transformers pass power (voltage times current), not voltage or current.

If I have a 1200 watt 120 volt heater, it will draw 10 amps. If the power company's lodal distribution voltage is 12,000 volts, they will use a 100:1 step-down tranformer to deliver 120 volts to me. That transformer will step down the 10 Amp current I require by a factor of 100:1, so on their side of the transformer, there is only 0.1 Amp, and 0.1 Amp times 12,000 volts is still 1200 watts. (Real transformers aren't 100% efficient, so the power company might actually have to deliver 1250 watts rather than the 1200 watts a perfect transformer would require.)


120The idea is that a different load is used with the different voltages. As a simple example:

  • on 120V: a 120V/120W lightbulb is 120 ohms (when hot) and draws 1 amp.
  • on 240V: a 240V/120w lightbulb is 480 ohms (when hot) and draws 1/2 amp.

In both cases, the load is 120 watts but by doubling the voltage, we get away with 1/2 the current, allowing smaller wires.

Similarly, we could start out with the 240V 1/2A, put that into a 2:1 transformer, and get out 120V 1A for the 120V lightbulb. For the 240V section of the transmission, we can reduce the wire size due to the lower current. Now scale this up to 10KV transmission lines going into 120V/240V residental wiring.

  • \$\begingroup\$ Alternatively, with lower current keep the same size wires, which will reduce the power lost in the transmission lines. \$\endgroup\$ – Pete Becker Apr 3 '13 at 21:55
  • \$\begingroup\$ Thank you that makes sense. However I still don't fully understand. Does this mean that house resistances are higher or that extra resistance is added in series in order to reduce the current. The latter seems counter productive as power would be lost to the extra resistance. \$\endgroup\$ – Deadly Cactus Apr 3 '13 at 22:00
  • \$\begingroup\$ The former. If you have two houses, one on 120V mains and one on 240V mains, and both are drawing the same wattange, the 240V house has 4 times the resistance as the 120V house. 240V lightbulbs, appliances, etc, are designed to have trice the current draw as comparable 240V items. All of this, of course, is greatly simplified, ignoring AC effects, transmission/transformer losses, etc. \$\endgroup\$ – DoxyLover Apr 3 '13 at 22:48

Power is the product of voltage and current:

\$ P = IE \$

Double the voltage and half the current, and the power remains the same. Or, double the current, and half the voltage. We can trade voltage for current, or current for voltage, and not violate the law of conservation of energy, because the power remains the same as long as the product \$ IE \$ remains constant.

It might make more intuitive sense if you think of mechanical power, instead of electrical power. Power is also the product of force and velocity:

\$ P = Fv \$

You can lift something heavy with a lever, but you will have to move the lever faster if you want to accomplish the same amount of lifting in the same amount of time. Or, you can move something far with a lever, but you will have to push harder.

Ohm's law is not violated because a transformer also transforms impedance, like a lever can transform the apparent weight of something. The transformers used in the AC distribution system are electrical levers, with a net effect like this:

lever analogy

By adjusting the turns ratio of the transformers between the power plant and the electrical load, we can move the fulcrum of this lever in either direction. Insulation is cheaper than conductors, so we put the fulcrum close to the power plant to minimize cost.


protected by W5VO Apr 3 '13 at 23:39

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