∫∫ AC vs. DC Power

Ever wonder what the difference between AC and DC power is, and why we use AC for everything? Well, you have come to the right place.

DC power stands for Direct Current. 5 amps of DC means that at any given second, 5 amps of current is flowing through the line. If that current is at 12 volts, which is standard for DC lighting circuits, you would have 60 watts of power, since 5 times 12 is 60. (Background reading: Power = Volts * Amps)

AC power stands for Alternating Current. 5 Amps of AC is a little more complicated. 5 Amps of AC means that a sine wave with a RMS value of 5 is flowing through the power. What the heck does that mean? Well, a picture is worth a thousand words:

In the above picture, we see a sine wave. In this case, the sine wave is of voltage not current over time, but they look exactly the same. You can see that the voltage wave crosses zero twice every 16.67 milliseconds, returning to its original position. This means that in one second the wave starts over 60 times (1 second divided by 0.0167 seconds/cycle gives 60 cycles). This is why our electrical grid is said to be at 60 Hertz, because the sine waves that our AC power system uses repeat themselves 60 times every second.

Now, look closely at the graph. You can see the peak voltage is 170 volts, but the RMS voltage is only 115 volts. Two questions arise: first off, what is RMS? Secondly, why should we care? I’ll answer the second question first.

We care about RMS because that is the voltage, or current, anything being subjected to a AC power “feels”. What does it mean to feel something? Well, if you’re a person and you stick your finger into an electrical outlet, you feel a shock. Because the voltage peak of 170 volts lasts only a fraction of a second, and because the sine wave crosses zero so many times, you do not feel a 170 volt shock. You feel some sort of average of 170 volts and zero. That average turns out to be 115 volts.

The same thing goes for a toaster, refrigerator, or light bulb. They heat, cool, and light things like a constant average, even though they are being given current and voltage as little waves.

Okay, so the peaks do not matter so much, the average matters. How come we use RMS instead of the average, and what is RMS anyway? RMS stands for Root Mean Square, and it is the square root of the average of the squares of the values of the sine wave over time. A lot to swallow? Well, yes, but it’s surprisingly easy to calculate. In a sine wave, the RMS equals the peak value divided by the square root of two. (I derive this here.)

Great. So now we know why we care and how to calculate the RMS. Why do we use AC power to begin with? Great question.

There are three things you need to know to answer this. 1) Power equals Current times Voltage, or P = I * V. 2) Losses in a transmission line are equal to the current squared times the resistance in the lines, or I2 * R. 3) Transformers can swap voltage for current by utilizing changing magnetic fields.

P = I * V is important because it means you can get the same amount of power through a transmission line if you double the voltage and cut the current in half. Because electrical losses go like current squared, this gives you the same amount of power with one fourth the losses. Pretty snazzy! In fact, when the electrical grid first started, Edison’s power grid was all DC power, and Westinghouse’s power grid was all AC. The entire world’s electrical grids are now AC because Westinghouse won the economic battle against Edison.

Westinghouse was able to win this battle by using transformers. He upped the voltage on his electrical grids an enormous amount, reducing current and hence reducing losses, but still delivering the same amount of power to his customers. Westinghouse was able to do this because AC power is always changing, which means the magnetic field around it is always changing. Transformers can only work with changing magnetic fields. Because Edison’s grid was DC, the magnetic field surrounding his lines was constant, so he could not use transformers. Thus, Westinghouse’s grid had far lower losses and was much cheaper to operate, and now the entire world uses AC power.

Is this a good thing? Well, yes and no. It means our transmission system is efficient – losses in the US average around 8-10 percent throughout the year although they can be much higher during peak times. On the other hand, solar cells naturally create DC power and are at a disadvantage since they must then convert their power into AC after it is created, suffering losses and increasing costs. Wind turbines can generate AC power directly, but it is easier and cheaper for them to generate DC.

Now, through advances in power electronics, methods exist for increasing the voltage (and decreasing current) in DC circuits. This means we are now starting to see high voltage DC power lines (HVDC), lines which both aid renewable energy generation and maintain low transmission losses.

3 Responses to ∫∫ AC vs. DC Power

  1. Thanks such a lot of for your work in writing this article. I am hoping for the same effective job from you down the road also!

    Reply

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