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."

9.4 Inductive Reactance

This is the fourth 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 fourth section of this module is titled, "Inductive Reactance."

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

1. The book thus far has only considered counter-EMF with a direct current (DC) source and a coil. With such a source, opposition to a change in current stopped once five time constants passed and the current reached a maximum or zeroed out.

But when the current has an AC (alternating current) source, the situation is different. A counter-EMF will constantly be in play from a coil and there will always be an opposition to the current, known as reactance. Reactance is symbolized by the letter X and with an inductive cause, X_L.

Because reactance is opposition to current flow, it is measured in ohms (Ω) just like resistance is. But while resistance is a permanent feature to a circuit based on its physical features, reactance changes based on the frequency of AC or the inductance of the circuit.

2. Reactance in a circuit caused by inductance is called, "inductive reactance." Its value is X_L = 2πfL, where f is the frequency in Hertz (cycles per second) and L is the inductance in henrys (volts per 1 amp change of current per second) .

Increased frequency means a greater rate of change and therefore a greater reactance.

Similarly, if the inductance is increased by increasing the number of turns in the coil, the size of the cross-section, or the permeability of the core, then the reactance to changing current increases as well.

So when inductance goes up, the reactance goes up.

9.3 The Universal Time Constant Chart

This is the third 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 third section of this module is titled, "Using the Universal Time Constant Chart."

9.1 Rise and Decay of Current and Voltage
9.2 LR Time Constant

The so called universal time chart gives the percentages of maximum I (current) or E (voltage) for each of the five time constants it takes for a circuit with an inductor in it to reach the maximum when powering up or to reach zero if powering down. The chart is to the right.

The time constant, as we learned in the previous section, is calculated by dividing the inductance by the resistance. So you can see on the chart that TC1, TC2, TC3, and so forth are expressed as L/R, 2L/R, 3L/R and so forth.

The line that starts at zero and increases to 100% is the powering up line. So at one TC (time constant), the voltage or current will be at 63.2% of its maximum value. At T2, it will have reached 86.5% of its maximum value, and so forth.

The line that starts at 100% and decreases to 0 is the counter-EMF coming from the inductor as the circuit powers down (E_L). It has the percentages opposite the percentages on curve A. So at one time constant interval, the circuit will still have 36.8% of what its maximum voltage was. At T2, voltage will be down to 13.5%. At T3 it will be at 5%. At T4 you will have 2% left. Then final at T5 the circuit will have completely powered down.

9.2 LR Time Constant

Last week we began 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.

9.1 Rise and Decay of Current and Voltage

1. The second unit for this week is called "LR Time Constant." L of course stands for inductance and R for resistance. "In a purely resistive circuit, current reaches its maximum value the instant the circuit is energized" (30). On the other hand, we have seen that inductance in a circuit creates a counter-EMF when a circuit is powered up, meaning that current will take a moment to reach its maximum value.

2. Now enter the notion of a "time constant." The time constant is defined as the inductance in henrys divided by the resistance in ohms, the result of which is in time.

TC = L/R

As it turns out, this constant approximates one fifth of the amount it takes for an LR circuit to energize up to its full current value. So it takes a circuit five time constants to power up. For each passing time constant, a circuit will move 63.2% of its remaining current amount.

So the first TC period, the circuit will go from zero amps to 63.2% of its final amp value. Similarly, when powering down, a circuit will go from 100% to 36.8% of its maximum value. In the second TC period, it will power up 63.2% of its remaining amount or another 23.3% to 86.5% of its maximum value (or down to 13.5% its maximum value if it is decreasing).

From T2 to T3, it will reach 95% of its maximum (or 5% if de-energizing). From T3 to T4 it will reach 98% (or 2%). Then by T5 it will be approximately to its maximum (or zero if de-energizing).

3. The section ends here, but I can mention the mathematical basis for this peculiar set of percentages. The underlying formula from which 63.2% comes is (1 - 1/e).

9.1 Rise and Decay of Current and Voltage

So it's on to Module 9 of the Navy Basic Electricity and Electronics series from the 1970s. The previous modules have been:

• Module 1: Current
• Module 2: Voltage
• Module 3: Resistance
• Module 4: Measuring Current and Voltage in a Series Circuit
• Module 5: Relationships of Current, Voltage, and Resistance
• Module 6: Parallel Circuits
• Module 7: Combination Circuits and Voltage Dividers
• Module 8: Induction

Module 9 is titled, "Relationships of Current, Counter EMF, and Voltage in LR Circuits."

1. The first unit is rather simple to summarize, it would seem. The diagram to the left gives a circuit that has a three way switch. When the switch is on one, no current runs through the circuit. When it is on two, the circuit powers up. When it is then on three, the circuit powers down.

From the previous module, we know that an inductor coil such as that pictured in the circuit diagram to the left will oppose the increase of current when the current powers up. Then it will oppose the decrease in current when the circuit powers down. The first section of the book gives us a diagram to represent this dynamic.

2. So the bottom axis is the time axis: T0, T1, T2, etc. The bottom part of the chart represents current. The middle of the chart represents the voltage in the resistor (which represents the total resistance of the circuit rather than a literal resistor). Then the top part of the chart represents the counter-EMF induced by the inductor.

If there were no inductor, the current and voltage would immediately jump to 1 amp and 10 volts respectively. But because of the counter-EMF of the inductor, it takes a moment of sorts to reach capacity. Meanwhile, you can see that the counter-EMF is maximum at the moment the circuit is closed and then is also maximum immediately when the voltage is turned off.

8.4 Inductance and Induction

Here's the fourth and final installment of Module 8, Induction, in Navy Basic Electricity and Electronics series from the 1970s. The first three units were:

8.1 Electromagnetism
8.2 Inductors and Flux Density
8.3 Inducing Voltage

1. Inductance is the property of a circuit that opposes any change of the current. Last entry we learned this idea as "Lenz's Law": "The voltage induced in a circuit by changing current always opposes the change causing it" (87). This opposing voltage is sometimes called "counter EMF" or CEMF for short.

This principle reminds me of Newton's third law: "A body in motion wants to stay in motion, and a body at rest wants to stay at rest." So with inductance. When current is decreasing, inductance wants to maintain it. When current is increasing, inductance wants to resist it.

The unit of inductance is the henry. 1 henry is the amount of inductance that yields one volt when the current is changing at the rate of 1 ampere per second. The symbol for inductance is L. The abbreviation for a henry is h, and it often appears in small quantities like the millihenry (1/1000) and the microhenry (1/1000000)

2. Computing inductance is done using the same formulas we used to calculate resistance.

• In a series circuit, the total inductance is simply the sum of all the individual inductors. 
• If a group of inductors in parallel all have the same value, then the total inductance is simply the inductance of one inductor divided by the total number of conductors in parallel.
• If you have two inductors, then the total inductance is L₁ x L₂/L₁ + L₂.
• If you have more than two inductors in parallel with different values, then the total inductance is the reciprocal of the sum of the reciprocals of all the inductors.

3. The amount of inductance for a coil depends on its physical characteristics.

• The greater the number of turns of the coil increases inductance.
• The larger the cross-sectional area of the core, the greater the inductance.
• The greater the permeability of the core, the greater the inductance.
• The longer the core material, the lower the inductance.
• The greater the space between coil turns, the lower the inductance.

4. Inductance is the capacity of a coil to oppose a change in current. By contrast, induction is the actual creation of a voltage, which requires motion. Inductance does not require current flow. Induction does. Induction is the action of inducing a voltage when current is changing in a circuit.

So the six factors which affect induction are

• the number of turns in the coil
• the cross-sectional area of the core
• the permeability of the core material
• the length of the core (inversely)
• space between the coil turns
• the rate of change in current flow

4. The changing current in one circuit can induce voltage in another circuit, which is called mutual inductance. This is also measured in henrys. The symbol for mutual inductance is M. Two coils can be positioned next to each other so as to exhibit mutual inductance.

The amount of mutual inductance is affected by their proximity, for this determines the percentage of flux lines of one coil in the turns of the other coil. This percentage is called the coefficient of coupling.

8.3 Inducing Voltage

Here's the third installment of Module 8, Induction, in Navy Basic Electricity and Electronics series from the 1970s. The first two units were:

8.1 Electromagnetism
8.2 Inductors and Flux Density

1. From an earlier module, we learned that three factors were necessary to induce an EMF in a conductor:

• a magnetic field
• a conductor
• relative motion between conductor and field

This leads us to Faraday's Law: "The EMF induced or generated in a conductor is directly proportional to the rate at which a conductor is cutting the magnetic lines of flux."

2. As current starts through a conductor, it generates a magnetic field, so two of the three conditions for generating an EMF are satisfied. Motion does actually take place because the lines of electric flux start at the center of the conductor and move to its outer part. As the flux moves on each half toward the outer part of the conductor, the lines are moving in opposite directions, satisfying the third condition until current is flowing through the whole wire.

In the meantime, the expansion of the current to fill the wire creates a "counter EMF" or CEMF. For a moment, the resisting EMF reduces the current briefly. The momentary CEMF is almost equal to the source voltage.

When the current is turned off, the same phenomenon occurs. The field collapses, causing relative motion. This time the generated EMF wants to keep moving in the same direction as the current was flowing.

3. If there is a conductor in another circuit, near the first one, a current will be generated in it by the first circuit. The direction of the induced current will be in the opposite direction. This is called Lenz's Law: "The direction of an induced EMF tends to set up a current whose magnetic field is the opposite of the original current."

A DC circuit will only generate current in the second circuit when it is powering up or down. An AC circuit, on the other hand, because it's value is always alternating, will constantly generate current in the second circuit.

8.2 Inductors and Flux Density

Here's the second installment of Module 8, Induction, in Navy Basic Electricity and Electronics series from the 1970s. The first unit was:

8.1 Electromagnetism

1. Flux density is the strength of a magnetic field around something, for example a coil. There are four factors that directly affect flux density and one that inversely affects it.

2. The first factor is the "permeability" or "reluctance" with which magnetic flux can pass through a material. If the core of a coil is an iron rod (more permeable), then there will be a significantly greater flux density of the magnetic field than if the core is simply air (, say with the coil wrapped around a cardboard cylinder.

The symbol for an inductor with either an iron core or an air core is as follows:

iron core conductor                            air-core conductor

3. The second factor that increases flux density is the number of turns in the coil. The more the turns, the greater the magnetic force.

4. The third is the cross-sectional area of the core. The bigger the cross-section, the greater the flux density. This is the opposite of the fifth factor, which is the length of the core. The longer the core, the less the flux density.

5. Finally, the amount of current flowing through the coil directly affects the flux density. The more the current, the greater the flux density.

8.1 Electromagnetism

I've finally made it to Module 8 of the Navy Basic Electricity and Electronics series from the 1970s. The previous modules have been:

• Module 1: Current
• Module 2: Voltage
• Module 3: Resistance
• Module 4: Measuring Current and Voltage in a Series Circuit
• Module 5: Relationships of Current, Voltage, and Resistance
• Module 6: Parallel Circuits
• Module 7: Combination Circuits and Voltage Dividers

Module 8 is about Induction.

1. As we already know, whenever current runs through a conductor, it creates a magnetic field around the conductor. Magnetic lines of flux form circular patterns around the conductor. The "left-hand rule for conductors" says that if you wrap your left hand around a conductor with your thumb pointing in the direction of the current, the direction of your other fingers tells whether the lines of flux are going in a clockwise or counterclockwise direction.

Electricity flows from negative to positive in a conductor and a magnetic field loops from north to south around a magnet.

2. If you wind a conductor around something--say a cylinder of metal--you create a stronger magnetic field (and a definite north and south pole). Using the left hand rule, if you wrap your fingers around the cylinder in the way they are wound, your thumb will point toward the north pole of this magnet created by current.

By these observations, we are building toward understanding a new component we have not encountered yet--the inductor or "choke." It is a coil that is usually wrapped around an iron core.

3. A number of applications are mentioned in this section. The first is a "relay." A relay is used to control a high voltage circuit without being physically connected to it. A current in a low voltage circuit, when closed, causes a magnetic field to arise around a coil, which attracts a conductor on a higher voltage circuit in such a way that the other circuit closes and then current flows in it.

There are several reasons to want to energize a high voltage circuit without simply flipping a switch on it directly. One is the ability to do it by remote control. Rather than run high voltage lines from afar, you can run low voltage lines. This also increases the safety of the situation.

4. A second application is the electric bell. Coils are used such that when the circuit is closed, a magnetic field is created and an armature hammer is pulled to hit a bell. But when it is so pulled, it breaks the circuit and the magnetic field is broken. But when the field is broken, the iron connected to the armature hammer reconnects the circuit, causing the magnetic field to return and the armature hammer to hit the bell again.

This process will occur repeatedly and whatever rate you set up, calling the hammer to hit the bell repeatedly until the overall circuit is opened.

5. The two applications above used a fixed core. A solenoid relay uses a movable core. When the current is running through the coil, a magnetic field is generated which pulls the core into the coil (because the north-south pole created pulls the core into the south pole). If this core is connected to a spring, the spring can close a circuit.

This sort of solenoid relay is used to start a car. The ignition closes a low voltage circuit with the car battery, which pulls an iron core into a coil. As it moves, a spring closes a higher voltage circuit with the starter, which then starts the car.

6. Two symbols are often used in diagrams to show current flowing in or out of a conductor. A dot suggests that the current is flowing out of the conductor, like the tip of an arrow. An x suggests that current is flowing into the conductor, like the back part of an arrow.

7.3 Voltage Dividers

This is the final section of Module 7 in the Navy Basic Electricity and Electronics series, a module on parallel circuits. The first two sections were:

7.1 Solving Complex Circuits
7.2 Voltage Reference

1. A circuit can be divided up in a way that provides different voltages to different parts of the circuit. Such a circuit is called a "voltage divider."

The picture below is an example of the kind of circuit that divides off voltage in order to work lamps of various volts and amps. The first lamp needs 6 volts at 2 milliamps. The second needs 12 volts at 8ma.

How many ohms does each resistor need to be in order to supply the appropriate volts and amps?

2. So R₃ is called the bleeder resistor. You can generally estimate the bleeder current as one tenth of the total current elsewhere. Since 8 + 2 = 10 ma, we can estimate the bleeder current through R₃ as 1ma.

Since voltage is common in parallel and E = IR, then 6v = (1ma)R. R₃= 6 kilohms.

3. By this process one can go on to determine the value of R₂ and R₁ as well. The 1ma from R₃ combines with the 2ma from DS1 yielding 3ma in R₂. The 12V in DS2 minus the 6V over R₃ suggests there is 6 volts across R₂. E = IR, so 6V = (3ma)R₂. So R₂ = 2 kΩ.

4. We can follow the same process to solve for R₁, which turns out to be 11ma over 12V or 1.1 kΩ.

7.2 Voltage Reference

This is the second section of Module 7 in the Navy Basic Electricity and Electronics series, a module on parallel circuits. The first section was:

7.1 Solving Complex Circuits

1. This section largely looked at the difference in voltage depending on where you are measuring that difference in a circuit. Here I'm reminded of a distinction that was made earlier in the series. Technically, voltage is not the same as the electromotive force coming out of the battery. Voltage is a difference in potential.

So close to the negative post of a battery you have more electrons than you have at the positive post of a battery. The difference is the volts. Positive voltage means that the point we are measuring has fewer negative charges than the point to which we are measuring.

2. Some circuit components require "negative voltage," so circuits can be designed to supply both negative and positive voltages. Both of course have the same "zap," but one involves more electrons than the other.

symbol for ground

3. A ground is when part of the circuit runs through, say, the chassis of a car. The symbol for a ground is at the right.

Sometimes a ground doesn't complete a circuit but is a reference point. You can then measure different voltages between this point and other parts of the circuit.

The symbol for a connection to a chassis, perhaps used as a reference

Chassis ground

point is to the left.

4. A telegraph operated with a single wire over long distances, grounded at both ends. The sending telegraph connected the circuit for a short or longer moment, the ground completing the circuit on both ends, standing for a dot or a dash.

7.1 Solving Complex Circuits

You've all been waiting for Module 7 of the Navy Basic Electricity and Electronics series, especially since we finished Module 6 back in 2016. Module 7 is Combination Circuits and Voltage Dividers. The first section is "Solving Complex Circuits."

1. Complex circuits are circuits that are not entirely series or parallel, but some combination of the two. So they can also be called "combination" circuits or "series-parallel" circuits. First we review the rules for each kind of circuit.

Rules for Series Circuits

• Current is the same throughout the circuit.
• Voltage is additive (Kirchhoff's voltage law)--add up the voltage across each element to get the total.
• Resistance is additive--add up the individual resistances to find the total.
• Power is additive--add up the power used by each element to find the total

Rules for Parallel Circuits

• Voltage is the same in every branch of the circuit.
• Current is additive (Kirchhoff's current law)--add up the currents in each branch to get the total.
• Total resistance is more complicated. The total resistance is always less than the smallest resistance. If the branches have equal resistances, the total will be a single resistance divided by the number of branches. If there only two branches, you can multiply the two resistances and divide by their sum. For all situations, you can add up the reciprocals of each branch resistance and then take the reciprocal of that.
• Power is additive--add up the power in each branch to find the total.

2. You can guess that combination circuits simply play out the rules above in predictable ways. So, each branch of the overall circuit is its own little series circuit of sorts. Meanwhile, you could reduce all the branches of the circuit to what an equivalent, single element would look like in its place and suddenly you have an overall series circuit.

So you can redraw complex circuits in ways that reduce them to what equivalent, simple circuits might look like.

6.4 Troubleshooting Parallel Circuits

This is the final section of Module 6 in the Navy Basic Electricity and Electronics series, a module on parallel circuits. The sections so far are:

6.1 Rules for Voltage and Current
6.2 Rules for Resistance and Power
6.3 Variational Analysis

This final section is on troubleshooting problems with parallel circuits and is rather short. It consists of five experiments.

1. The first experiment involves voltage and shows that the voltage drop in each parallel branch is the same as the applied voltage at the source.

2. The second experiment has to do with current and shows that the total amperage is the sum of all the branch currents.

3-4. The fourth experiment has to do with a short in one of the branches of a parallel circuit. "Current follows the path of least resistance" (104). Accordingly, if there is a short, then all the current will go through that path. This will blow a fuse if one is in play.

If there is an open in one branch, it effectively disappears from the system. The voltage and resistance in other individual branches stays the same, but the total current will drop (and thus total resistance will go up).

5. A short can cause considerable damage to the other components of a circuit. The ohmmeter function of a multimeter can help locate a short, as there will be no resistance in that branch. (Fire and smoke may also help :-) De-energize circuit before measuring.

6.3 Variational Analysis

This is the third section of Module 6 in the Navy Basic Electricity and Electronics series, a module on parallel circuits. The sections so far are:

6.1 Rules for Voltage and Current
6.2 Rules for Resistance and Power

This third section is about how voltage, current, power, and total resistance change as voltage is increased or resistance is increased/decreased.

1. So the basic principles so far in this module are that

• Voltage is going to be the same in every branch of a parallel circuit.
• Total current is the sum of the current in every branch.
• The total resistance goes down if you add another branch.
• E = IR
• P = EI

So this section plays out a few scenarios.

2. What if you double the voltage from the source?

• Voltage in every branch will go up.
• Therefore, current in every branch will go up because I = E/R.
• Resistance will stay the same--it's a physical factor.
• Power will go up because P = EI.

3. What if you add another resistor in another branch?

• Voltage remains the same in every branch.
• There will now be current in that branch and since current is additive, the total current will go up.
• That means the total power will go up, since P = EI.
• Total resistance will go down, due to the reciprocal method.

4. What if you change the resistance in one branch, say decreasing it?

• Voltage remains the same in every branch.
• Current goes up in that branch because I = E/R.
• Therefore, total current goes up.
• Therefore, total power goes up.
• Since R_total = E/I and total current goes up, total resistance goes down.

6.2 Rules for Resistance and Power

This is the second week of Module 6 in the Navy Basic Electricity and Electronics series, a module
on parallel circuits. The first section was:

6.1 Rules for Voltage and Current

This second section now addresses resistance and power in parallel circuits.

1. In a series circuit, the total resistance is the sum of the individual resistances. In a parallel circuit, the total resistance will actually be lower than the lowest resistance in any of the branches. The total resistance is sometimes called the "equivalent resistance," as if you were to replace all the individual resistors with one.

When you add a resistor to a series circuit it increases the total resistance. When you add a resistor in parallel, the total resistance goes down. Accordingly, total current increases.

2. To find the resistance in any one of the branches, use the formula R=E/I for that branch. There are a number of other ways:

a. When each branch has the same amount of resistance, divide that number by the number of branches and you will have the total resistance (equal branch method).

b. When the branches have different resistance values, another method is the product over the sum: R₁ * R₂/R₁ + R₂.

c. Another method is the reciprocal method. You take the reciprocal of the sum of the reciprocals of all the resistances.

 3. Power dissipation is the same whether the circuit is series or parallel. The three power equations from the previous module were P = EI, P = I²R, and P = E²/R. Because power is the total heat loss, add up the power used by all the resistors. 

6.1 Rules for Voltage and Current

So we move on to Module 5 in the Navy Basic Electricity and Electronics series (here is the previous module). This module is on Parallel Circuits (as opposed to the series circuits of the previous module). The first section is "Rules for Voltage and Current."

Some take-aways from this first section:

• A parallel circuit is one which has more than one path for current to follow, although with only one common source.
• Each path provides a "load" with a certain resistance.
• Christmas lights used to be in a series configuration. If one light burned out, the rest wouldn't work. Most now are configured in parallel.
• The voltage across the branches of a parallel circuit will be the same in every branch. Voltage is not additive.
• This is different than in series circuits. For them, we had Kirchhoff's Law--"The sum of the voltage drops equals the applied voltage." Voltage is additive.
• On the other hand, the current--the amount of electrons passing a given point at a given time--is divided up among each branch. Branch current in each branch is determined by the amount of resistance in that branch. The total current equals the total current of all the branches.
• Kirchhoff's Current Law is that the total current is the sum of the current in all the branches.

5.5 Troubleshooting Series Circuits

This is the fifth and final week of Module 5 in the Navy Basic Electricity and Electronics series. This module is on troubleshooting problems in series circuits. The first four sections were:

5.1 Voltage, Resistance, and Current
5.2 Ohm's Law Formula
5.3 Power
5.4 Internal Resistance

1. Most of the problems that occur in a series circuit either come from a short circuit or an open circuit. A short circuit is where there is a current path that shouldn't exist creating more current than is desirable. An open is where a part of the circuit is not connected or not fully connected and thus the current is not flowing as it should.

There can be a direct short circuit and there can be partial shorts. A direct short circuit is where the poles of the power source are directly connected in some way to each other. This will likely mess up the power source. A partial short only by-passes some of the components.

2. The purpose of a fuse is to keep the components in a circuit from damage in the case of a short. The symbol for a fuse is:

Fuses are rated for the amount of amps that they can safely carry.

You can locate a short using either a voltmeter or an ohmmeter. The voltmeter will tell you if there is too much voltage. Meanwhile, an ohmmeter will read 0 when it shouldn't.

3. An open circuit can also be found either with a voltmeter or an ohmmeter. When an ohmmeter is measured across an open element, it will read infinity. A voltmeter will read nothing across parts of the circuit where the open is not. But it will read full voltage across the open component.

An open circuit often results from a blown fuse or a defective switch.

5.4 Internal Resistance

This is the fourth week of Module 5 in the Navy Basic Electricity and Electronics series. This module is on the relationships between current, voltage, and resistance. The first three sections were:

5.1 Voltage, Resistance, and Current
5.2 Ohm's Law Formula
5.3 Power

1. This week is on the internal resistance of a source such as a battery. Let's say that you were to put a voltmeter across a battery in an open circuit and it were to read 12 volts, the "no-load" voltage. Then lets say you close the circuit and the voltmeter drops to 11 volts. This suggests that your battery has an internal resistance that is zapping some of the force.

2. To measure the internal resistance (R_i) of a source:

• Measure the no-load voltage.
• Energize the circuit and then measure the voltage across the source again.
• Subtract the difference (internal resistance decreases the voltage in the circuit).
• Measure the current in the circuit.
• Use R=E/I to determine the internal resistance of the source.

3. Hopefully, the internal resistance of your source is small enough to be negligible.

5.3 Power

This is the third week of Module 5 in the Navy Basic Electricity and Electronics series. This module is on the relationships between current, voltage, and resistance. The first two sections were:

5.1 Voltage, Resistance, and Current
5.2 Ohm's Law Formula

1. "Power is the rate of doing work" (66), the amount of work done by the electricity (in this case) in a given time. We might express this relationship with the formula:

P = W/T

Another way to put it is to say that electrical power is the rate of converting electrical energy into some other form of energy (e.g., heat).

2. Electrical power is measured in watts (watts having the symbol w). A 100 watt bulb burns brighter, has less resistance, and dissipates more power than a 60 watt bulb.

3. Power equals voltage times current P = EI .

• If we substitute in E = IR from the previous lesson, we get P = I²R .
• We can also do a little algebra and come up with P = E²/R
• You use different versions of the relationships depending on what information is given.

*4. Read at your own risk. Another tidbit in this section is that the amount of heat produced by a resistor is the power times the amount of time or I²RT . If you think of the original formula P = W/T, this formula suggests that work relates in some way to the heat given off.

The section doesn't really explain what work is when it comes to electricity. I guess that is something for a later module. In terms of mechanical energy, work is the force times the distance. I am not remembering exactly how that plays out with electricity, but I seem to remember that the same unit of work is used, the joule.

5.2 The Ohm's Law Formula

This is the second week of Module 5 in the Navy Basic Electricity and Electronics series. This module is on the relationships between current, voltage, and resistance. The first section was:

5.1 Voltage, Resistance, and Current

1. You can calculate the current in a system without shutting it down and measuring it. You can use "Ohm's Law" if you know the voltage and the resistance. The formula is:

E=IR

The voltage equals the current times the resistance. We can rearrange the formula as well. Current equals the voltage divided by the resistance, and the resistance equals the voltage divided by the current.

2. You can use this formula for an entire circuit. You can also use it for a distinct part of a circuit.

3. There can be more complex situations where the value of one resistor is known but not the value of another. In such cases, knowing algebra will come in handy so that you can set up an equation and then solve for the unknown.