Year: 2012

Resistance in Circuits

The greater the resistance (R) of a circuit, the less current (I) will flow through it (an inverse relationship). The equation is:

Current = Voltage / Resistance

I = \frac{V}{R}

An actual resistor. This one is 330 Ω with a tolerance of 5% (you can tell from the colors of the bands). Resistors are used to slow down the current moving through a circuit. Image by Nunikasi, via Wikipedia.

Resistors can be actual resistors, lamps, toasters, or anything else that uses electricity. Even the wires have resistance (but we don’t usually consider that since it’s small compared to the resistance of the other stuff).

The total resistance of a circuit depends on the way the resistors are arranged:

  • Series:
    • Add the resistances.
    • R = R_1 + R_2
    • More resistors in series reduce the amount of current in the circuit. (dimmer lights)
  • Parallel:
    • Add the inverse of the resistances to get the inverse of the total resistance.
    • \frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}
    • More resistors in parallel increase the amount of current used by the circuit. (brighter lights).
Comparing resistance and current in parallel circuits. Arranging the same resistors in parallel uses 4.5 times as much current (and energy) in this example.

(Notes: Current is a bit like water flowing through a pipe. Resistors are blockages that slow down the flow. Put two blockages, one after the other, and you reduce the flow rate. If you put two blockages into two different channels then though each one slows down flow the total flow is larger.)

As you put in more and more parallel circuits you draw more and more current until you overload the circuit and the wires heat up enough to burn through their insulation. Fuses (or circuit breakers) are used to prevent this; they burn out, breaking the circuit, when too much current goes through them.

Questions:

  • Why are appliances in your house almost always connected in parallel and not in series?
  • Which bulbs will be brighter: two bulbs in series, or two bulbs in parallel?
  • What are the total resistances and the total current that runs through the two circuits in the diagram?
  • What is the total power used by the two circuits in the diagram? Remember, Power = Voltage × Current

Where the Trees Are

Map of Woody Biomass in the U.S. in the year 2000, by the Woods Hole Research Center, via NASA's Earth Observatory.

The Woods Hole Research Center put together this map of “Aboveground Woody Biomass” that essentially shows where the trees are in the U.S.. The map was created using, primarily, satellite imagery. Their website has a nice, interactive, version of the map, and a 3d video flyover of the of southeastern Georgia.

Trees build their woody biomass using carbon from the atmosphere (remember during photosynthesis plants absorb carbon dioxide gas), so these trees are represent stored carbon. If they are burned their carbon is released to the atmosphere. If more trees are planted then they will absorb more carbon dioxide from the atmosphere. This map serves as an inventory of what we have now; a baseline for discussions about what to do about carbon-driven climate change.

The Mississippi River flood plain shows up remarkably well because of it's lack of trees. Flood plains are great for agriculture.

The Magnetic Fields of the Planets

The Earth’s magnetic field results from the movement of molten metal in the Earth’s core. The outer core actually. It’s mostly molten iron, which conducts electricity, and as it convects up and down, like boiling water in a pot, the moving electrical charges create the Earth’s magnetic field. Its a bit like a dynamo.

The internal structure of the Earth. Movement in the liquid metal outer core (green arrows) generates the earth's magnetic field.

What drives the convection of the outer core? The heat released from the freezing of the liquid metal to the solid inner core. The inner core is ever expanding, and the outer core is getting smaller and smaller. Ultimately, when the entire outer core freezes the Earth’s magnetic field should disappear. But we’ve got some hundreds of millions of years left so we don’t have to worry quite yet.

The Other Planets

The question came up: Do Mars and the other planets have magnetic fields?

Astronomynotes has compiled a table of Planet Atmospheres and Magnetic Fields that shows that of the inner planets — Mercury, Venus, Earth and Mars — only the Earth has a significant magnetic field; Mercury does have its own field but it has less than 1% the strength of the Earth’s.

At present, Mars does not have a magnetic field, but it does have remnant magnetism imprinted on its rocks, indicating that it used to have one in the past. It’s internal dynamo died away long ago. Interestingly, the pattern of Mars’ remnant magnetism indicates that it’s interior was once molten enough that the surface had tectonic plates just like the Earth.

Comparison of Earth's healthy magnetic field and the local, remnant magnetism of Mars. Image via NASA.

On the other hand, the outer planets have much larger magnetic fields; Jupiter’s is almost 20 times larger than Earth’s. The gas giants’ magnetic fields are also generated by fluid motion in their interiors (Stevenson, 1983 (pdf)). It’s likely, however, that in some of these bigger planets, at least, the electrically conductive fluid is not liquid metal like in the Earth’s core, but either liquid hydrogen, or a water solution with dissolved electrolytes.

Jupiter's strong magnetic field interacts dramatically with its moons, inducing magnetic fields in some. Image via NASA.

Drawings of Jupiter

Étienne Trouvelot's drawing of the planet Jupiter from 1880 (via the New York Public Library), combined with an image of the planet from the Cassini spacecraft taken in 2000 (NASA/JPL/Space Science Institute)

The New York Public Library’s website hosts a remarkable collection of Étienne Léopold Trouvelot‘s astronomical drawings by that date back to 19th century.

The beauty and detail of these illustrations are a remarkable testament to the intersection of art and science.

Mare Humorum. From a study mad... Digital ID: TROUVELOT_006. New York Public Library

Building a Simple Electric Motor

This is a really simple electric motor that only requires some wire, a battery, and a magnet. Simon Quellen Field has a wonderfully detailed description of how to build the motor, and some elegant tips on how you can make the motor run faster.

My middle-schoolers quite enjoyed building one of these, and I’m planning on having my high-school physics students also try it; only a couple of them claim to have done it before. It should be a good way to tie together electricity and magnetism.

(Evil Mad Scientist has an even simpler motor, but, given that the risk that their homopolar motor is quite capable of launching a drywall nail across the room, I think I’d suggest not trying that one without extremely close supervision.)

Although it’s a bit trickier, another great way of demonstrating electromagnetic induction is to build a simple alternating current generator that runs a small light bulb.

Bill Beaty’s website explains how to build the generator in excellent detail.

The best part of building the generator is that you can actually feel the extra energy it takes to light the bulb, as you spin the magnets.

How Primary Elections Work

C.B.P. Grey explains how primary elections work. Right now the Republican Party is conducting its primaries to choose a candidate to face Pres. Obama in the November general elections, and all their debates, as well as the sequence of primaries highlighting different parts of the United States, provides for a quite interesting view of the social and political diversity in the country. The video below, however, focuses on the details of the voting process.