## Tuesday, July 30, 2013

### Ohm's Law

"Eee equals eye are". That's it. That's Ohm's law. Or this way:

E=IR

Voltage equals current times resistance. It's the law.

If you take Ohm's law and divide both sides by R, this is what you get:

E/R=I

So if you know the voltage and the resistance, you can figure the current.

Or instead, if you take Ohm's law and divide both sides by I, you get this:

E/I=R

So if you know the voltage and the current, you can figure the resistance.

The nice thing is, you don't have to remember three different formulas. You only have to remember Ohm's law and be able to rearrange formulas. Pretty neat.

But you do need to know how to rearrange formulas. Maybe that escapes people, I don't know. It's not hard; you just have to do it a lot to have confidence in it. I did.

Here's another formula you can rearrange, from Tejvan Pettinger:

Take GDP at the prices we pay to buy it (that's called "nominal" GDP, for some reason) and divide it by what economists call "real" GDP (which is what GDP would have cost if prices never went up at all). You're left with a measure of the change in prices. (Then multiply by 100 so the numbers are not so tiny.)

Let me translate Pettinger's formula into the terms that FRED uses:

• For "Nominal GDP" use GDP
• For "Real GDP" use GDPC1
• For the "GDP deflator" use GDPDEF

When I replace Pettinger's values with FRED's values, the formula looks like this:

The FRED graph of it looks like this:

 Graph #1
The first title across the top of the graph is GDPDEF, which we have on the left side of the equal sign in the formula above. That's the blue line on the graph.

I made that blue line extra-wide, because FRED draws it first. So, when it draws the second line, the red line, you can still see the blue line behind it. You can see the two lines follow the same path. The two lines -- as our formula says -- are equal.

The second title across the top of the graph is same the calculation we have on the right side of the equal sign in the formula above.

We can rearrange the formula to get GDP ("nominal GDP") all by itself on one side of the equal sign, and all the calculation on the other side. Multiply both sides by GDPC1 ("real GDP"), and divide both sides by 100, to get GDP:

The FRED graph:

 Graph #2
The expression on the left side of the equal sign in our formula is restated in the first title line of the graph, and appears as the blue line on the graph. The expression on the right side of the equal sign is restated in the second title line , and appears as the red line on the graph.

Again you can see the two lines are identical, confirming what the equal sign in the formula tells us.

So we've looked at the "GDP Deflator" by itself, and "nominal GDP" by itself. All that's left is "real GDP" or GDPC1. Again, we can rearrange the formula to get it. Starting with the formula just above Graph #2, to get GDPC1 by itself on the left side of the equal sign, we have to divide by GDPDEF. To make sure things left and right of the equal sign stay equal, we have to divide stuff on both sides of the equal sign by GDPDEF. Then, to get rid of the 100 and get GDPC1 by itself, we have to multiply both sides by 100. That gives us this:

And again, at FRED that looks like this:

 Graph #3
The graph shows that our rearranged formula is correct. The two identical lines indicate that the quantity on the left of the equal sign is equal to the quantity on the right.

By convention, usually the complex calculation is shown on the right side of the equal sign, and the simple variable is shown on the left. It's sort of like the final step, when you're rearranging formulas. But it's not just a convention. It helps you understand what you're looking at, when you're figuring it out for yourself. I left it out, above. So really, the formula just above Graph #2 should look like this:

Rearranging formulas isn't hard. You just have to do it a lot to have confidence in it.