Current

        Like people, the most interesting charge is the charge that is in motion, moving about rather than sitting still.

• Charge in motion is referred to as current.

        Current can exist in many different physical forms because there are many different physical situations in which charge can flow. 

• The most common manifestation of charge in motion is the movement of electrons in a wire such as the wire leading to the computer that is running this lesson. That''s one form of current.  Here''s a simulation that lets you see how charge flows around an electrical circuit through several elements.  Click the green button to see that.

• However, ions in water carry charge and a current can flow in water with ions in solution.  Standing in distilled (ion-free) water near an electrical outlet in your bathroom is nowhere near as dangerous as standing in tap water with some ionic content, but do not try the experiment.
• Charged particles moving in a vacuum are another manifestation of current, and you experience that every time you watch television or look at a computer screen.  Charged particles fly from an electron gun at the back of a picture tube or a monitor tube, strike the screen and you see the light emitted from the screen as a picture.
• Even ink-jet printers charge the ink blobs in the jet, and the jet is an example of a current!

Goals For This Lesson

        There are lots of different forms of current, and you need to understand current - the flow of charge if you want to understand the electrical devices you use.

        Objectives for this system include the following:

  For yourself

  To develop a mental model that helps you picture and understand current in an electrical circuit.

  In an electrical circuit

  Be able to define and measure currents in any element. 
  Be able to use units of current correctly.

       There are a number of different ways of thinking about current.  In different situations you might want to use different ways of thinking about current to help you figure out what''s going on. 

• Water flowing in a pipe is analogous to current.  The water flows in the interior of the pipe, and current actually flows through the empty spaces between atoms in a wire, but the analogy can be useful.  It helps if you have some sort of analogy that lets you use something you already know about to help you think about new things like current.
• Current is an information carrying signal.  There will be times when you don''t care so much about the charge that''s being transported as current flows but you will care about the information that is being sent using current.
• There will be times when the charge that is being transported is what is important, and there are times when you will have to think in a backwards sort of way about that.  Semiconductor engineers do this all the time when they talk about holes moving in semiconductors.  They have invented a concept that is based on missing electrons and the spaces they should occupy in an atomic lattice, and they work with ideas of missing electrons - holes - that move about in semiconductors.

        Most of the time, when you are dealing with current you are dealing with electrons moving through metallic wires of electronic devices.  At this point, we will begin discussing electron flow through wires.

        Current usually flows through wires, and electrical engineers usually idealize the situation.  The figure below shows a wire carrying current, and the idealized representation we use - the arrow that points in the direction the current flows.  Note that the current in the idealization is symbolized by an arrow along the idealized wire, and the arrow points in the direction that positive charge flows.

 In fact, electrons are flowing the opposite way, but we imagine current as a flow of positive charge.

        We want to emphasize the concept of current as a through variable.  Whenever we speak of current we specify the area that it flows through. The figure below shows a current flowing through a rectangular cross section wire.

If we imagine the wire split in the middle (along the divider shown) then the current is split between these areas. If the total current is twelve amperes, then six amperes will probably flow through each half of the rectangular wire.  That''s shown below.

Later, when we consider electrical elements - like resistors - we will want to consider elements in parallel, and you will need to understand this situation.  If the two halves of the conductor above are considered to be resistors, then they are in parallel in the picture above.  We could connect something at either end of the conductors and current would split entering the parallel conductors, and could come together when exiting the parallel conductors. 

Current - continued

        Current is charge in motion.  To be more precise, consider the situation below.  If we imagine "slicing" the wire, we can then count the rate at which charge flows through the slice.  That''s shown with the slice and arrow below.

        Hopefully, it is clear that the flow rate of charge through the slice is measured in couloumbs/second.  However, couloumbs/second has another name, amperes.  Current is usually measured in amperes (really coulombs/second!).  So, to measure the current passing through the wire, you can "sit" on the dark gray slice and watch charge (coulombs) move past the slice, count the coulombs that pass in a give amount of time, then divide the number of coulombs by the time interval to compute the current.

Problems

1.  Now, here''s a question for you.  Let''s imagine that you have a wire, and you somehow observe that 2 coulombs passes through the wire in one second.  Click on the button you think gives the value of the current.

2.  You observe charge going through a wire for 4 seconds, and you find that 20 coulombs passes.  What is the current? 

       Now, if you reallly understand what current is you can turn this around.  In the problems above you were given the charge passing through a wire in a given amount of time.  Turning that around we can ask a different question.  If we have a constant current, I, flowing through a wire, then we can compute how much charge flows through the wire in some given time interval.  Say we have the following situation:

I = Current = 3.2 amperes

Time interval = 15 seconds.

        Then we would know that the amount of charge that flowed through the wire in the 15 second time interval would be:

Total charge = 3.2 amperes x 15 seconds 
          = (3.2 coul/sec) x 15 sec 
          = 48 couloumbs 

Problem

3. Here''s a problem for you.  You have a car battery, and you leave on an interior light.  The light draws one ampere from the battery.  How many couloumbs will flow through the light if you leave it on for three hours? 

Comments on the Problem

        If you think about the problem above you see that a couloumb is a pretty small amount of charge.  For example, the car battery can probably supply one ampere for somewhere between 50 and 100 hours.  That''s a lot of couloumbs!  Manufacturers who make car batteries use other units of charge.  Since:

Charge = Current x Time Interval

we can use other units.  For example, the time interval can be measured in hours.  Then, instead of couloumbs we would measure charge in units of ampere-hours.  Electrical engineers don''t use that unit often, but battery manufacturers use it all the time.  A car battery that can provide one ampere for 80 hours is rated at 80 ampere-hours.  Of course, it can also provide 80 amperes for one hour. 

Problem

4. Here''s another problem for you.  How many couloumbs are there in one ampere-hour? 

5. Here''s still another problem for you.  You have a 50 ampere hour battery.  How many couloumbs of charge are stored in the battery if it is fully charged? 

6. Here''s one more problem with the same battery as you saw above.  You have a 50 ampere hour battery.  If you draw a constant half ampere (0.5 ampere) from the battery, how long will it continue to supply current?  Give your answer in hours. 

7. Here''s one more problem with the same battery.  If you have a trickle charger that can supply 200 milliamps, how long will it take you to charge the battery fully?  Give your answer in hours. 

Is that a reasonable time?

8. Here''s another problem with the same battery.  If you have a a device that draws one ampere and it comes on for ten minutes in each hour, how long (in hours) will the battery supply current for your device?  It''s important to know this because your device is measuring weather data on a mountain top, and in deep snow, so you need to know how long it will last. 

9. Here''s the last problem with that battery.  Shown below is the current drawn by a device.  How long (in hours) will the battery supply current for this device?

Facts About Current - Units

        There is one last point you need to know.

• Current - like every other physical variable - has units.  Current is really charge flow, so the units for current are in terms of charge/time.  In the MKS system that is:

Current units = charge/time = couloumbs/sec = amperes.

        The most commonly used unit it the ampere, and it is often referred to as amps.  If we have a current of 3.5 amperes, we would say:

I = 3.5 amp or I = 3.5A

Facts About Current - Polarity

        When you have a circuit and you want to figure out how the circuit will behave you will generally try to determine what the currents and voltages in the circuit are going to be.  That prediction is what you want.  However, before you can calculate a current you need to have a precise definition of what you mean by the current, and that''s where you get involved with polarity.  We will introduce the idea of polarity with a question for you to answer. 

Question

Q1.  In this circuit, Willy Nilly wants to determine current I₅.  He has defined that current as shown below at the left.  Is that the correct definition of the current?  Or is the current definition at the right the correct one?  (Note, depending on visual space in your browser, the right one may display below the left one so the buttons are labelled Left/Top and Right/Bottom.)

        The point to the question above, is that when you are analyzing a circuit, the way current polarity is defined is entirely up to the person who is analyzing the circuit.  (That''s unless your instructor asks you to use a particular polarity, or a textbook problem defines the polarity for you.)  Polarity definitions are arbitrary.  Make sure that you always are clear about how you define polarity - both for current and for voltage.  Otherwise, you may work a problem and find I₅ = 7A, and someone else may find -7A.  You could have a long argument only to find out that you and the other person defined polarities differently. 

Facts About Current - Summary

        Let''s review things a bit.

• Like water flowing in a pipe, current flows in a wire.  Just as the water in the pipe is confined to the pipe, the charge flowing in a wire is confined to the wire.  It can''t get away, and stays within the wire surface.
• Like water flowing in a pipe, charge has to go somewhere.  So, in fact, it flows through electrical devices, going in one terminal and out another.
• When current flows for a time charge flows.  Current is the rate of flow of charge, so you can determine how much charge flows from the current and the time it flows when the current is constant.

Measuring Current

        Current flows through something.  Current can flow through a wire, the normal situation, but it can also flow through an ionic solution, through the ground, and many other things.  The important word here is through. Current is a through variable. Current always flows through something.

        What this means is that in order to measure current you need to get the current to go through a meter.  An ammeter is the type of meter used to measure current.  In this section we''ll talk about measurement of current and using ammeters.

        Here''s a diagram of a circuit with an ammeter inserted to measure a current.  There are many different currents flowing in this circuit.  We are interested in current I?, which flows through element 3.  We want to measure current I?.  (We call it I? because that''s the one we want to know.)

        Now, if we want to measure that current, we have to get it to flow through through an ammeter - a device that measures current.  The way we do that is to break the circuit between element 3 and element 4 and insert an ammeter in series with element 3.  We say that two elements are in series whenever the current that goes through one element is forced to go through a second element.  Note that all of the current going through the first element (element 3 here) goes through the second element (the ammeter here).  Here''s a circuit diagram that shows where the ammeter goes.

        The important thing here is to see how the ammeter is inserted so that the current you want to measure is made to flow through the ammeter.  When that current flows, the ammeter will measure the current.  Here, current I? flows through the ammeter after flowing through element 3 and before flowing into element 4.

        Here''s a pictorial representation of an analog ammeter.  It''s typical of ammeters.  It has two terminals.  They are usually red and black.  When you have one red terminal and one black terminal, you can be sure that the ammeter will read a current like the one defined in the picture.  When the current, I, shown in the figure, is positive, then the ammeter needle will read upscale indicating the measured current.

        Now, here''s a representation of a digital ammeter.  It''s going to have the same kind of terminals.  The difference here is that it will give a digital value for the measurement, showing the measurement result with an LED display.

        There''s nothing very complicated about measuring current.  You need to get the current you want to measure to flow through an ammeter which will then measure the current.  In principle it''s pretty simple.

Problem

10.  Here is the same circuit where we introduced you to the ammeter.  We kept the ammeter in the same place.

We placed the ammeter there in order to measure the current through element 3.

• Does the ammeter also measure the current through element 4?

• Does the ammeter also measure the current through element 1?

A Note On The Discrete Nature Of Charge

        There''s one other item to consider.  Charge comes in discrete packets but it is often useful to assume that it can take on continuous values.  That lets us bring all the power of calculus to bear when we discuss current. Current is the flow of charge, and it is thought of in terms of a quantity of charge flowing through an area in some small amount of time.  However, we often want to drive that concept to the limit, by imagining a current at an instant.  Then, we imagine letting the time interval shrink to zero so that we think of current as a derivative:

i(t) = dQ(t)/dt

        We do realize through all of this that charge comes in discrete packets, and that this limit is ultimately mathematical nonsense.  Still, the charge of an electron is so small that we can think in these terms in most practical situations.  When we consider more complex circuits it will be helpful if we think, however, in terms of charge that can take on continuous values.

Using Current - Where Do You Use Current?

        You use current every time you use an electrical appliance of any sort.

• If you own a car, you own a storage battery.  The battery stores enough energy to allow you to start your car. The battery stores energy by storing charge on the battery plates.  When you use the battery, charge flows out of the battery.  That''s current flowing from the battery.
• When you plug an electrical device into a wall plug you use current.  One example is a light bulb.  Current flows from the wall plug, through the connecting wire and through the bulb.  In the process, the current heats up the filament in the bulb generating light - unless it is a fluorescent lamp, and then a different process creates the light.

What if the Current isn''t Electrons in a Wire?

        The most common kind of current you will see will be electrons flowing in a wire.  That''s what you''ll see 99% of the time.  However, any time any form of charge flows, that''s a current.

        Here are a few examples of currents.  Current - a flow of charge - is what happens when you have any of the following, and it is not an exclusive list!

• Ions in motion in water - What would happen if you managed to connect an electrical outlet to a sink full of water.  Ions, however, also move in car batteries and electroplating solutions.
• Charged blobs of ink in an ink-jet printer.
• Electrons moving through space - For example, the electrons striking the computer screen to generate the picture seen as this is written on a computer

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