9.5 Relationships in Inductive Circuits

This is the fifth week of Module 9, "Relationships of Current, Counter EMF, and Voltage in LR Circuits." These modules are part of the Navy Basic Electricity and Electronics series from the 1970s. The fifth section of this module is titled, "Relationships in Inductive Circuits."

9.1 Rise and Decay of Current and Voltage
9.2 LR Time Constant
9.3 Universal Time Constant Chart
9.4 Inductive Reactance

1. The previous units have set out a number of relationships. For example, the "reactance" of an inductive circuit, the equivalent of its resistance, is found by the equation X_L = 2πfL, where f is the frequency of alternating current and L is the inductance.

So we can substitute X_L for resistance in the earlier equations.

• Since E = IR, then E = I * X_L
• Since I = E/R, then I = E/X_L
• Since R=E/I, then X_L= E/I

2. In normal circuits, power equals current times voltage, P = EI. Or substituting in for E, P = I²R.

In a purely inductive circuit, power is never consumed, but we can speak of "apparent power." It is symbolized by P_a, and it is measured in volt-amperes (va), not watts.

What happens is that the power is supplied by the AC source, stored for part of the cycle in the inductor, and then returned to the source. The amount of volt amps stored in the inductor is called the reactive power (P_x). In a purely inductive circuit, it is the same as the apparent power. We say it is measured in "vars," "volt-amps reactive."

3.1 What is resistance?

We now move on to Module 3 of the Navy Basic Electricity and Electronics series. The first two modules were:

1. Electrical Current
2. Voltage

Today starts the booklet on resistance.

• If current (electron movement) and electromotive force (resulting in voltage, a difference in potential throughout a circuit) are two key elements of a circuit, resistance is a third factor always present.
• "Resistance is the property that opposes current flow" (6).
• Resistance is symbolized by R and the unit is the ohm, symbolized by Ω.
• Conductors have low resistance, insulators or non-conductors have high resistance.
• Some factors that determine resistance include the nature of the material (atomic structure), the area of the cross-section (e.g., of wire), and the length (e.g., of wire). The larger the cross-section, the less the resistance. The longer the wire, the more the resistance. Atomic structure determines how many free electrons are available to move around.

That's the big picture. Here are some additional details.

• One ohm is the amount of resistance that allows 1 amp to flow through a circuit when one volt is applied. 1 amp per volt.
• Resistance is sometimes needed to limit the current flow to a safe value through a circuit. Completely unopposed current can lead to a "short circuit," which is damaging. 
• The resistance of a toaster or iron or bulb is what provides the heat or light. 

2.1 Electromotive Force (EMF)

This week starts Module 2 of the Navy Basic Electricity and Electronics series. Last week I finished summarizing:

Module 1: Electrical Current

The second module begins with Electromotive Force (EMF) produced by chemical action. This book was written in the early 1970s so it's fun to see how out of date the batteries it has in mind are. Of course the way chemistry works hasn't changed. Here are the bullet points from the first section of this Module:

• Electromotive force (EMF) is the force that moves electrons through a circuit, created by some source like a battery.
• Voltage is related but slightly different. EMF is a force. Voltage is the difference of potential between the positive and negative poles of the battery or source of EMF.
• The module references "dry cell" batteries. The figures are funny because they go back to when both the positive and negative posts of a battery were on the top, the positive in the center and a negative terminal on the outer rim of the top.
• In that scheme, there was a center rod in a battery that was made out of something like carbon. 
• Then the outer "electrode" on the inside of the container might be made out of something like zinc. 
• Then a chemical paste in the middle was an "electrolyte" that facilitated an accumulation of electrons on the zinc electrode, leaving a positive charge on the carbon rod.
• Today, of course, the most common batteries are lithium batteries.
• So within the battery, there is the potential for an electron flow from the positive to the negative terminals of the battery.
• Outside the battery, there is the potential for an electron flow from the negative terminal around a circuit and back to the positive terminal.
• A "volt" is the unit of measurement for potential difference. The same metric prefix applies for volts as for amps (milli-, micro-, kilo-, mega-)
• Batteries can be connected together in series to add up the total amount of voltage (negative to positive, negative to positive, etc).
• When not connected properly (in series opposition as opposed to series aiding), they cancel each other out.
• When connected in parallel, the life of the battery is increased (often done in subs, at least in days gone by).

Next Week: 2.2 Magnetism

1.4-5 Measurement of Current and the Ammeter

Today we finish the first module of the Navy Basic Electricity and Electronics course from the early 70s. The module has been on Electrical Current. Previous review posts have included:

1.1 Electricity and the Electron
1.2 Electron Movement
1.3 Current Flow

We finish today with sections 4 and 5.

Here are the bullet points to remember from section 4:

• When you add more battery cells in a series, a light bulb burns with greater intensity. More "current" is flowing through the bulb.
• When we measure current, we are in effect measuring the (net) amount of electrons going past a given point at any given time.
• A "coulomb" of electrons is 6,250,000,000,000,000,000 electrons (6.25 x 10¹⁸). Discussing electrons in groups this large makes it easier for us to talk about them.
• The measure of current is called an amp (for ampere). 1 amp of current is one coulomb passing any point in a circuit per second. 1 amp = 1 coulomb per second.
• I is the abbreviation for current or number of amps. a is the abbreviation for amps. The symbol for charge or coulombs is Q. So I = Q/T.
• This section also introduces scientific notation. Especially important are micro (10^-6) and milli (10^-3).

Section 5 is then relatively brief by comparison. It deals with the tool used to measure current.

• An ammeter is used to measure current.
• An ammeter needs to be connected in "series," which means that all the current has to run through it.
• the positive lead of the ammeter should connect to the positive side of the circuit and the negative lead to the negative side. In other words, "observe polarity."
• De-energize the circuit before connecting the ammeter. Then re-energize. Also de-energize before disconnecting.

Next week: 2.1 Electromotive Force

1.3 Current Flow

I've been reviewing the Navy Basic Electricity and Electronics course from the early 70s. Previous review posts have included:

1.1 Electricity and the Electron
1.2 Electron Movement

Today's module is on "Current Flow."

Here are the bullet points to remember from the second module:

• Random drift (previous module) of electrons doesn't do any work. What we want to do work is a "directed drift" of electrons, an "electron flow," also known as "current."
• To have electron flow, we need a complete circuit, a "closed circuit," a complete path for the electrons to follow all the way from the source, through a path, and back to the source. Electricity can't flow in an "open circuit," where there is a break in the path.
• This path needs to be made out of a "conductor," that is, a type of material in which electrons flow relatively easily (a path made up of an "insulator" material won't be much help at all).
• The content of the rest of this module largely has to do with the symbols for some basic items you might find in a "circuit diagram" or a "schematic." A circuit diagram is a way of drawing an electrical system using symbols for things like batteries, light bulbs, and switches. 
• The diagram at the bottom is an example of such a diagram. I have labeled the items.
• For the battery symbol, the negative side is the shorter line. Electricity flows from the negative, around, and back to the positive terminal of the battery.

Next Week: 1.4-5 Measurement of Current and the Ammeter

1.2 Electron movement

Last week I started reviewing the Navy Basic Electricity and Electronics course from the early 70s. Last week was:

1.1 Electricity and the Electron

Today's module is on "Electron Movement."

Here are the bullet points to remember from the second module:

• Protons are said to have a positive charge and electrons a negative charge.
• Like charges repel; opposite charges attract.
• So the negative electrons are attracted to the nucleus by the positive protons. [1]
• The neutron has a neutral charge.
• In an atom like copper (which in its neutral state has 29 electrons), some electrons are closer to the nucleus than others. 
• The outermost electrons are sometimes knocked out of an atom. What's left of the atom then becomes a charged "ion" (because it has lost some negative).
• The process of becoming an ion is called "ionization" and the amount of energy necessary to cause ionization is called the "ionization potential."
• The random drift of "free electrons" in a wire doesn't do anything. They need to be pushed.

Next week: 1.3 Current Flow

[1] The electromagnetic force between these charges helps keep the atom together. Another force, the "strong nuclear force" keeps the protons together, even though their charges should repel them. The strong nuclear force only works over a very short distance, but it is stronger than the electromagnetic force that would otherwise push the protons apart.

1.1 Electricity and the Electron

1. In 1980, when I started my freshman year in high school, I signed up for an elective I think was called "Electronics 1." It was with Mr. Richard Brandt, a delightful if shall we say slightly overweight teacher. It was a different sort of class.

I suspect most of the students were on a vocational track. It was geared around the kinds of things you would need to know to be an electrician. In my third year I built a power supply and circuit board that I still have. Radio Shack has long stopped selling the kinds of transistors, resistors, diodes, and capacitors of that day, which was right on the cusp of integrated circuits.

I needed three slots in my circuit board for one Radio Shack transistor in 1983. Now an iPhone 8 has 2 billion of them on a chip. Sigh.

So we worked at our own pace through a series of self-directed Navy Basic Electricity and Electronic books (you can now download them for free). The books were from 1972 (or earlier) and were initially designed for electricians in the Navy. For example, some of the first module talks about the kinds of batteries they used to have on submarines.

My old friend Casey Walker and I made a number of visits to the public school Book Depository our senior year and snatched a host of the textbooks we'd had in high school. I think that's where I nabbed all the Navy modules I'd gone through in two and a half years with Mr. Brandt.

In my plot to take over the universe, I've been reviewing a lesson each weekend and thought I'd blog down study notes for future review. These books are so tedious. The questions are painfully simple but it asks you the same questions over and over and over in slightly different ways. It's learning... and death... by repetition.

2. So Module 1 (i.e., book 1) is called "Electrical Current," and Lesson 1 is about "Electricity and the Electron." Here's the scoop:

• Electricity does work.
• All matter is made up of atoms. Atoms are very, very small. They are so small that they are the stuff of theory rather than direct observation (although now see this).
• At the center of an atom is a clump of small "particles." The clump in the center is called the nucleus, and the particles are called protons and neutrons.
• Most of the space around the nucleus is empty. The third basic "particle" in an atom is about 100,000 nucleus lengths away. It's called an electron.
• Electrons thus surround the nucleus. You might start by thinking of planets surrounding the sun, although that's not quite right. Electrons are much, much smaller than protons (about 1/1845 as massive)
• So atoms are made up of protons, neutrons, and electrons.
• Electricity is the movement of electrons through a medium.
• Wires are solid. They don't have holes in the middle for the electrons. :-)
• Different kinds of atoms have different numbers of protons. (For example, copper has 29 protons in its nucleus. Most copper atoms have 34 neutrons in their nucleus. And in its neutral state, copper has 29 electrons.)

Next week: 1.2 Electron movement.