07.18.2019: Math Notebook Ch. 16

Today’s soundtrack is Dream Theater: Images and Words, one of the most incredible albums ever made. If you haven’t yet heard it, do yourself a favour and go listen to this prog metal masterpiece.

This afternoon, I’m reading Chapter 16 of Everything You Need to Ace Science in One Big Fat Notebook, “Electricity and Magnetism.”

Electricity and magnetism are similar: both are produced by positive and negative charges in matter interacting with each other.

Electricity is produced by negative and positive atoms interacting with each other: negatively-charged atoms are attracted to positively-charged atoms; as the electrons flow, we get electricity.

Negative atoms have more electrons than protons; positive atoms have more protons than electrons. We call atoms with a positive or negative charge ions; neutral atoms (which have the same number of protons as electrons) are just called atoms.

Electrons can easily jump between atoms. When an object has many negatively-charged ions present, that object is holding a static charge. A quick transfer of electrons from one body to another is a static discharge.

Because negative ions repel other negative ions, putting a negatively-charged object against a neutral object can temporarily repel the electrons in the neutral object, creating positively-charged ions, resulting in the negatively-charged object clinging to the now positively-charged object. An example given is a balloon given a negative charge by rubbing it in one’s hair, then sticking the balloon to the wall through this process called induction, whereby the balloon’s electric field influences its surroundings.

Some materials are better than others at conducting electrical charges. Those which are good at conducting electricity are called conductors; those which insulate against the flow of electricity are called insulators. Anyone who has played or watched Pokemon knows that Pikachu is strong against water types and weak against rock types; this is because water is a good conductor of electricity, and rock is an insulator.

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There is a third medium that’s somewhere in between insulators and conductors: resistors. These “[resist] the flow of electrons but still [let] them through” (p. 162), resulting in heat and/or light. We use resistors to make toast and to light our homes. Sometimes resistance is caused inadvertently: the longer a wire is, the more resistant to the flow of electricity it will be.

We measure electricity’s movement as electric current by calculating how many electrons move past a given point per second as amperes. Electric currents come in two varieties: alternating current and direct current (AC and DC). The former is made of “a flow of electrical charges that alternate direction periodically” (p. 163); the latter is made of charges that “move in one direction the entire time” (p. 163). A wall outlet in one’s home produces AC; a battery produces DC.

To keep an electric current constantly flowing, we set it up in a loop. This circuit is made of a wire which is attached to the positive side of the power source. The wire continues on and connects to the “load,” which is what we call the device being powered. Next, the wire goes on to meet the switch, which we can use to keep the circuit open or we can break the circuit, which will turn off the power. Finally, the wire goes from the switch back to the power source, this time connecting with the negative side. The negative charge “pushes the electric charges around [the] circuit” (p. 166), keeping the electricity flowing.

There are two kind of circuits that we can use: series and parallel. In the former, we get a basic closed loop – it’s easier to set up, but there are a couple of downsides. First, the loads earlier in the circuit get more power; second, if one of the loads breaks, the circuit breaks, and nothing will get power. Those old Christmas lights where if one burnt out, the whole thing died? Series circuit. Such a pain. Anyway, in a parallel circuit, there is one main loop set up like an oval, and there are wires connecting across. In the middle of each “shortcut” across the main loop are the loads. The advantages are twofold: The loads all receive equal power, and if one of the loads dies, the remaining loads still receive power, because there is still a way for the electrons to flow through the conductive wire.

Remember learning about potential energy? Much like a book on the shelf, electrons have potential energy. Their potential energy is calculated based on how many volts a power source has. The more voltage a power source has, the higher the potential energy of the electrons in its circuit. We can determine the number of volts that a power source has by finding what the difference in power is between the positive and negative ends.

Now that we know about resistance, current, and voltage, we are in a good position to understand Ohm’s law, which tells us that the voltage of a circuit is the product of current and resistance. “Voltage is measured in volts (V), current in amperes (A), and resistance in ohms (Ω)” (p. 168).

We can also us current and voltage to determine the electrical power of a circuit. Power is measured in watts; it tells us how fast electricity is turned into heat or light or kinetic movement – for example, a battery-powered pink bunny banging a drum. We can calculate the power of a circuit by multiplying its current by its voltage. If an electrical current is not producing power, electrical energy is conserved.

I mentioned a battery-powered toy in the above paragraph. How do we go about converting electricity into kinetic energy? By use of a motor, which is “a device that converts electric energy into kinetic energy” (p. 171) through the use of magnetism. Both magnets and electricity have positive and negative charges; both magnets and electricity have fields of influence around them. Any wire with a current flowing through it also has a magnetic field around it. We can harness this: when we wrap coiled metal around a current-carrying wire, we amplify the magnetic field. We can use this stronger magnetic field to make a wire spin, which provides kinetic energy.

What if we want to do things the other way around? What if we have kinetic energy that we want to turn into electricity? We can either move a magnet around in a coiled wire, or we can “[move] a wire through a magnetic field” (p. 171). Either method will create an electric current. We can also use a generator: a gasoline-powered engine that “spins a loop of wire through a magnetic field” (p. 171). This process is called electromagnetic induction.

Summary:

  1. The south pole of a compass needle points north.
  2. If two wires are placed next to each other and both of them have a current running through them, the electricity from the wires will attract the two wires to each other because a wire with an active current creates a magnetic field.
  3. An electric field’s influence will decrease with further distance and will increase with more charge.
  4. If I install a new bulb with a higher resistance than the old bulb, the new bulb will be brighter (assuming the battery doesn’t change), but the current will be lower.
  5. An atom has a negative charge when it has more electrons than protons.
  6. If I place a negatively charged hairbrush close to my hair, my hair will get a temporary positive charge through induction.
  7. The resistance of a wire increases decreases as it gets wider.
  8. The resistance of a wire increases as it gets longer.
  9. If Christmas tree lights are wired in a series, and one burns out, all of the other lights go out too.
  10. If Christmas tree lights are wired in parallel, and one burns out, all of the other lights stay on.

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