How is Alternating Current (A/C) more efficient for long distance transmission of electrical energy?

Question

In mathematica terms?

Answer 1

The conversion of electrical power into heat — that is, transmission losses — depends solely on the current flowing in a wire, not on the voltage. Since electrical power is the product of the current times the voltage, you can transmit electricity over very long distances with very small losses if you make the voltage huge and the current tiny.

With DC, this is purely a hypothetical thought; you'd have to generate the electricity at tens of thousands of volts and then pipe it in to homes at the same voltage! This is very dangerous, and not in any way desirable.

However, alternating current can be altered with a transformer into a higher or lower voltage, arbitrarily. The power level through a transformer is unchanged, so if you increase the voltage ten times (for example), the current is reduced to 1/10 — and so are the transmission losses!

Thus, by using transformers to convert AC into tens of thousands or hundreds of thousands of volts, it's possible to send the power very far indeed with acceptable losses. This would be nearly impossible with DC.

Answer 2

Let's say the power plant is supplying 1KW to your house at 100V (not 110V just so that the calculations are easier)

The current required to do this 1000W/100V = 10 A

Let's say the resistance of the cable from the powerplant to your house is 5 ohms. You woud have lost I^2R watts in the transmission, ie., 10 * 10 * 5 = 500 W lost.

With AC it is very easy to step up or step down the voltage using transformers. When you do this, if V1 and I1 are the input voltage and current, and V2 and I2 are the output voltage and current, then for the transformer, V1*I1 = V2 * I2

Let's say the power plant steps up the voltage to 10000 V and then just before reaching your house, steps it down to 100.

The current consumed at your house at 100V is 10 A
Therefore 100V * 10 A = 10000V * x A
where x is the current along the transmission line
x = 100 * 10/10000 = 0.1A

Again, assuming the line resistance was 5 ohms, the total power wasted along the transmission line is I^2R = 0.1 * 0.1 * 5= 0.05 W compared to the previous example where 500 W was lost delivering 1000 W to your house.

This is a rather simplistic picture, but generally illustrates why AC is more efficient thanDC, where you cannot efficiently and easily step up and step down the voltage.

Answer 3

It's easy and more efficient to step up or step down AC current than DC.