How Much Electricity Do Christmas Use?

December 23, 2013 by  

How Much Electricity Do Christmas Use?, Most people that are putting up Christmas decorations have already finished the task. Of course, if you are a business or a city you probably put up lights before Halloween – I have no idea why. So, of course I want to estimate how much money these lights cost to run over the holiday season. Let’s get to work.

To start, I will get an idea of how much power a strand of Christmas lights uses. There is this fairly awesome device, the Watts Up Pro. Basically, you plug different devices into it and it tells you the power that device uses. The other cool thing is that you can plug it into your computer and record changes in power using Vernier’s Logger Pro software.

Here is a fairly standard string of 100 lights with the Watts Up Pro.

That’s 44.7 watts for 100 lights or 0.447 Watts per tiny bulb. What about the whole tree? Well, I could just estimate the number of lights on there but I lost track. My wife really likes lots of lights. I feel bad for saying this, but I measured the power – 508 watts. BOOM. That is way more than I expected. If I assume all of the bulbs are 0.447 watts, this would mean there are over 1,000 lights on that darn tree.

What else do we have Christmas lights on? Well, the kids have small trees in their rooms and there is another small tree by the door along with a lighted wreath. This puts our indoor Christmas lights at around 800 watts. Just for a comparison, my coffee pot uses about 650 watts while making coffee and my refrigerator averages to under 100 watts over a day.

What about the outside lights? For me, I am at 474 watts. This means that my Christmas spirit consumes around 1,300 watts. I am killing the planet with my spirit.

Estimating the U.S. Cost
Now for the estimation part. With any estimation, you have to make some assumptions. Here are mine:

You can see that I included variable names for these estimates so that I can write down my calculation as an equation (then the values can easily be changed). OK, first, how much energy was used? Remember that power is the rate of change of energy:

Using my estimates for lights, I can write the U.S. energy usage for Christmas as:

Then the total cost would simply be this energy times the cost per energy. However, my energy is in Joules, or watt*seconds. I can convert this energy cost into dollars per joule:

This puts the cost at:

Just make sure that c is in the correct units – also Tavg needs to be in seconds, not hours. Putting in my estimates, I get an electricity cost of $233 million. That’s not too bad. I mean, it’s a lot of money – but this is the USA we are talking about here. I would compare this to the energy saving by switching out of Daylight Saving Time – but I fail to see how to get a good estimate for that.

What About the Griswold Christmas Lights?
I hate that one of my favorite Christmas movies is Christmas Vacation because it isn’t really appropriate for the whole family. But it sure is funny. So, what about Clark’s lights on his house? How much would that cost?

First, there is an important difference with the Griswold house. Clark Griswold apparently uses the old-style Christmas lights. You know, the ones with the big and hot bulbs. I don’t have a string of these lights to measure. However, I did find a bulb that looks similar in a Christmas night-light. It runs on 6.3 watts.

But how many lights does Clark use? That’s a tough one. Let’s start with a bulb area density. If I assume the door in the screenshot above is 2 meters tall, I can get an estimate for how many light bulbs are used per square meter. With some basic counting, I am going to go with 20 bulbs per square meter. The main roof of the house is about 15 meters wide – but there is also a garage that is maybe 4.5 meters wide. I will just estimate the total roof area at about 19 meters by 10 meters. Let me include another 30 square meters to account for the lights on the front of the house (assuming no lights on the back). This puts the light-covered area at 220 m2.

How many light bulbs? This would be (220 m2)*(20 bulbs/m2) = 4,400 bulbs. If each bulb is 6.3 watts, the total power would be 27.7 kilowatts. There are lots of different estimates out there for the household power uses. An estimate (averaged over a day) is probably between 500 and 1,000 watts (but not during Christmas). That might seem like a low estimate, but remember that for probably half the day, there isn’t much going on in the house (electricity-wise). So Clark’s house is clearly beyond the norm.

How much would this house cost to power the lights? Well, first, Clark probably paid the 1989 electricity rates. I’m not sure what those rates were, but they had to have been lower than 10 cents per kilowatt hour. If he ran that exact setup with today’s rates for 4 hours, that would cost $11 a day – or 4.6 cents per minute. It seems like in the movie, he put the lights up fairly close to Christmas so maybe he only had these lights up for a couple of weeks.

What if Clark used the smaller lights that are popular now? These aren’t as bright, so he would probably have to double the light density to maybe 40 lights per square meter. Assuming a power per bulb of 0.447 watts this would give a total power of 3.9 kilowatts and a cost of $1.56 per day.

I should have also looked at the LED lights, but I didn’t have any of those to test (yet).

But what about the current going through this outlet?

From the movie, it seems like all of the lights are plugged into just this one outlet (and that was the reason he couldn’t get the thing to work). What kind of current would this have? In terms of current, I can write the power as:

Of course, with household circuits, both the current and the voltage are alternating at 60 Hz. If I use the root-mean-square current and voltage (RMS), I get the RMS power (which is what the Watts Up Pro gives). Oh, what the heck is up with using RMS? Well, if you plot the voltage (or current) as a function of time, it is positive half the time and negative half the time. If you averaged the current over one whole cycle, guess what you get? You get zero amps. So, the trick is to square the current and then find the average. After that, you can take the square root of this squared average. It gives a non-zero value that is a good representation of the average current.

In the U.S., the standard outlet RMS voltage is 120 volts. With this, I can solve for the RMS current. If the lights use 27.7 kWatts, this would be a current of 230 Amps. Is that high? Oh, yes. Very high. A typical high-current device like a vacuum cleaner is typically less than 10 amps. According to Wikipedia, it looks like the highest-current circuit breaker trips at 125 Amps. So … how did Clark Griswold get his outdoor lights to even work? Who knows? Maybe he shorted out the circuit breaker – which would be dumber than giving Jelly of the Month as a gift.

How hot would the wires get? OK. So, the extension cord that Clark plugs in looks like a standard cord. First, these things are only rated for like 13 Amps, not over 200 Amps. But it looks like they are about 16-gauge wire inside with a diameter of 1.291 mm. So, let’s say I have 1 cm of this wire. What resistance would it have? Using the resistivity of copper (ρ), I can find the resistance:

At room temperature, copper has a resistivity of 1.68 x 10-8 Ω*m. So, my 1 cm section of wire would have a resistance of 0.00128 Ω. Notice that if the wire had no resistance at all, it wouldn’t get hot. Also, as the wire gets hotter, the resistivity goes up too. I’ll just stick with this one value for now.

Now, let’s say I run current through this wire for 60 seconds. Now that I have the resistance of this little piece, I can calculate the power it dissipates (by having resistance).

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