chapter25

//**Electric Current and DC Circuits **// Listen up children, and allow the experts to teach you about electric currents. This will probably be the most important thing you learn in your high school career, so pay close attention. In a weird world, everything is related to the flow of current. In this section of the E and M curriculum, we will begin to explore just how the currents that pervade your life actually work. Be warned, all the symbols and variables may look scary at first and the theories and rules may be hard to visualize, but trust us... We won't lead you astray. So sharpen your pencil, grab a notebook, and try not to fall asleep !



//** E**// //**lectric Current**//

Current is, in short, electrons moving through a conducting (usually metal) rod. While in reality the path of the electrons (negatively charged particles) defines the current, all physics calculations deal with the direction a positive charge would move.

The measure of current deals with how much charge crosses a plane per unit of time. Current (I) is measured in Amperes. 1 Ampere (A) = 1C/s. In formula form, the following are useful to keep in mind when working with currents:

Now, in real life, direct current is more rpesent than you would think. In most low-voltage cases, direct current installations are common. For devices usuallly powered by a battery, only direct currents flow through the circuit (as opposed to the alternating currents that appear in other cases..This dark magic will be discussed later in the cirriculumn by another brave Pioneer). Additionally, solar-powered voltage sources exclusivley produce a DC current. Therefore, as this growing "green energy" trend grows in the US, so does the presence of direct current in real life! Isn't physics applicable in everyday life?!

//[[image:http://i321.photobucket.com/albums/nn380/lolilpopgal/1291594561jpg.gif]] Resistance//
== ==

Above, you can see three forms of Ohm's Law, a super important law if you want to get any questions about circuits right. It's basically saying that the current (I) is equal to the voltage source or potential difference (V) divided by the resistance of the system (R). Resistors resist (duh) the flow of charge and cause the voltage to drop when current passes through it. Resistors are really really important because they make sure that stuff doesn't blow up. For a greater understanding of resistors, please read on to understand how resistors varry in resistivity and then move onto the current analysis section to see how these resistors affect a circuit!

//**[[image:http://i321.photobucket.com/albums/nn380/lolilpopgal/1291594561jpg.gif]] Resistivity**//
Now, it is important to understand that resistivity varies from material to material. The resistivity of an object depends on two things:


 * 1) <span style="background-color: #ffffff; color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">The material it is made of
 * 2) <span style="background-color: transparent; color: #000000; display: block; font-family: 'Times New Roman'; font-size: 16px; text-align: left; text-decoration: none;"><span style="background-color: #ffffff; color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">The shape of the object

<span style="background-color: transparent; color: #000000; display: block; font-family: 'Times New Roman'; font-size: 16px; text-align: left; text-decoration: none;"><span style="background-color: #ffffff; color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">For example, take a copper wire and a glass fiber of the same shape (same length and area). The glass has a much greater intrinsic resistance than does the copper, so its resistance will be greater. This only holds for certain when the length and area are the same length, though. Resistivity, R, is determined not only by the intrinsic resistivity of the object, rho, but also the length and cross-sectional area of the material at hand. The formula for resistivity is as follows:

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">If you are curious, the following table of resistivity may be very helpful to glace over when problem solving for your teacher... Enjoy!

===<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 150%;">//** Electric Currents & Drift Speed**// ===

<span style="background-color: transparent; color: #000000; display: block; font-family: 'Times New Roman'; font-size: 16px; text-align: left; text-decoration: none;"><span style="background-color: #ffffff; color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">Current exists when there is a net motion of charge in a wire. Understanding this, consider a wire at any given time. At any given time, millions of electrons are zooming around in random directions, however due to the random motion, there is no net movement of charge. Thus, there is no current.

<span style="background-color: transparent; color: #000000; display: block; font-family: 'Times New Roman'; font-size: 16px; text-align: left; text-decoration: none;"><span style="background-color: #ffffff; color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">Now consider the attachment of a voltage source, such as a battery. The voltage source provides an emf, electric motive force, driving the flow of charge. The emf isn’t truly considered a force; it’s the work done per unit of charge and is measured in volts.

<span style="background-color: transparent; color: #000000; display: block; font-family: 'Times New Roman'; font-size: 16px; text-align: left; text-decoration: none;"><span style="background-color: #ffffff; color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">Also, it is critical to understand the flow of current. It starts with the Electric Potential energy provided by the positive terminal of the emf, travels through the circuit, reaches the negative terminal of voltage sources with zero potential energy, once again gains EPE from the voltage source and goes through the circuit again. <span style="background-color: transparent; color: #000000; display: block; font-family: 'Times New Roman'; font-size: 16px; text-align: left; text-decoration: none;"><span style="background-color: #ffffff; color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">Also relating to electric current is drift speed. Drift speed is the magnitude of the velocity as they drift along the wire. The direction is opposite to the direction of the electric field. Therefore, drift speed only exists when there is an applied electric field. The formula for drift speed is as follows:

<span style="background-color: transparent; color: #000000; display: block; font-family: 'Times New Roman'; font-size: 16px; text-align: left; text-decoration: none;"><span style="background-color: #ffffff; color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">n = Number Density (number of free charge-carrying particles per unit volume in a cross sectional area A) <span style="background-color: transparent; color: #000000; display: block; font-family: 'Times New Roman'; font-size: 16px; text-align: left; text-decoration: none;"><span style="background-color: #ffffff; color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">q – Charge on each particle <span style="background-color: transparent; color: #000000; display: block; font-family: 'Times New Roman'; font-size: 16px; text-align: left; text-decoration: none;"><span style="background-color: #ffffff; color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 90%;">V d = Drift

<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 150%;">//** Energy and Power**//

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">When a carrier of positive charge drops by an amount V in potential, it loses potential energy is the amount qV. IF this happens in time t, then the rate at which the energy is transferred is given by the equation:



<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">Combining with V = IR, we have…



<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 150%;">//** Circuit Analysis**//

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">For now, all the work you will do with Circuits will contain connecting wires, batteries, and resistors. The resistance in an ordinary metal wire is negligible; therefore the resistors control the current. When a resistor is present, all the resistance of the system is concentrated on that resistor.

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">Before we start, please not that the following denotes resistors:

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">And the following denotes batteries (voltage source): ==

==

<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 150%;">//** Combining Resistors**//

===<span style="color: #808080; font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">//**<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 120%;"> S eries **// ===

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">To find the total resistance of resistors in series, all you have to do is add them up!

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 14px;">For Example:



<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">However, when actually solving problems with resistors, it's important to keep two things in mind for series:

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">1. The **<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 14px;">voltage ** across resistors in series is **<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 14px;">not equal **, sadly. (It's equal to the resistance multiplied by the current!) <span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">2. The **<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif;">current ** across resistors in series is **<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif;">equal ** !

===//<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 120%;">**<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 120%;"> P <span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">arallel ** //===

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">To find the total resistance of resistors in parallel, you need to take the reciprocal of the sum of their reciprocals. That sentence sounds kind of confusing, but read it a couple of times, and it'll make sense. Or you can refer to the equation/example below:



==<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 14px; font-weight: normal; line-height: 21px;">Similarly, when actually solving problems with resistors, it's important to keep two things in mind for parallel: == ==<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 14px; font-weight: normal; line-height: 21px;">1. The **<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 14px; line-height: 21px;">voltage ** across resistors in parallel is **<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 14px; line-height: 21px;">equal **, yay! == ==<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 14px; font-weight: normal; line-height: 21px;">2. The **<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 14px; line-height: 21px;">current ** across resistors in parallel is **<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 14px; line-height: 21px;">not equal **. You can easily find the different currents by using V=IR ! Or in this case, I = V/R ==

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">Basically, the properties for voltage and current in parallel and series circuits are opposites. Don't get them mixed up, or else you risk getting a not-so-good grade on your next physics test on DC circuits. A helpful way to remember is that for <span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">**P** arallel, the <span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">**P** otential difference is the same. Get it? Since they both start with P. (Potential difference is another way of saying voltage). If that doesn't help at all, then too bad, just remember it! You'll really need this one, trust us (we are experts after all).

<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 150%;">//**[[image:http://i321.photobucket.com/albums/nn380/lolilpopgal/1291594561jpg.gif]] Kirchhoff's Rule**//
<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">When the resistors in a circuit cannot be classified as either in series or in parallel, you must use another method for analyzing the circuit. This method is called Kirchoff’s Rule… please consider the following rules:

<span style="color: #808080; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;"> **The Loop Rule:** The sum of potential differences (+ and -) that traverse any closed loop in a circuit must be zero.

<span style="color: #808080; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;"> **The Junction (Node) Rule:** The total current that enters a junction must be equal to the totally current that leaves the junction.

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">As these definitions can seem rather technical at first, I will walk you through them in a little simpler English.

<span style="color: #808080; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;"> Plainly, the //**Loop Rule**// if we start at a certain point and proceed through the circuit to return to the same point, we will have the same potential as we initially did. Even simple, this means that any decrease in Electric Potential Energy must be matched by an equal increase in Electric Potential Energy.

<span style="color: #808080; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;"> Similarly, the //**Junction Rule**// simply says that the charge per unit of time (current) that flows into a junction must equal the charge per unit of time (current) that is flowing out.

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">To help you out when problem solving, please keep the following in mind:
 * <span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%; margin-top: 0in;">When going across a resistor in the same direction as the current, the potential drops by IR
 * <span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%; margin-top: 0in;">When going across a resistor in the opposite direction as the current, the increases drops by IR
 * <span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%; margin-top: 0in;">When going form the negative to the positive terminal of a voltage source, the potential increases by that voltage
 * <span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%; margin-top: 0in;">When going form the positive to the negative terminal of a voltage source, the potential decreases by that voltage

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">Next, please take a look at the following exercise to help you fully understand Kirchoff’s Rule; this is best learnt by actually doing a problem.

<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 150%;">//** RC Circuits**//

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">Capacitors are typically charged by batteries. When a circuit is closed, the electrons are attracted to the positive terminal of the battery, leaving the top plate of the capacitor. Also, electrons accumulate on the bottom plate of the capacitor, continuing until the voltage across the capacitor is equal the emf of the battery. When this condition is reached, the current stops and the capacitor is fully charged.



<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 150%;">// Lab (Circuit Simulation)//

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">In the following lab, you will be asked to use your knowledge of Kirchoff’s rule and technology to explore the flow of current through a circuit.

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">First, please solve the following two circuits for Voltage, Current, and Power at all resistors.

This is what our math turned out:

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 14px;">Next, go to the Circuit Constructor applet in the high school shares files and recreate the above circuits. Then, on the applet, determine the Voltage, Current, and Power across all of the resistors on each circuit.

**<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif;"><span style="color: #008080; font-family: Tahoma,Geneva,sans-serif;">C ircuit #1: **

**<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif;"><span style="color: #008080; font-family: Tahoma,Geneva,sans-serif;">C ircuit #2: **

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 14px;">Now, compare your results for accuracy. If your results do not match up, check over your work both on paper and online to find your error!

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 14px;">Good work, now you hopefully have a better understanding of these physics concepts and how technology can be integrated into the classroom.

//<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 150%;"> Real World Applications //

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">Well, now that we have persevered through all that intensive math and physics, you can take refuge in the fact that this chapter actually has real life uses! ( If you're still awake ).

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">Take a look at what’s in your pocket. You probably have an iPod – it’s powered by a battery which sends a direct current through the device! That’s right, any electronic gizmo you posses that operates with a battery (a low-voltage source) uses a direct current to power itself! <span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 14px; line-height: 21px;">Now, just look up. See those lights? They are the most common example of a resistor in the world. Due to the resistance provided by the light bulb, light is produced, illuminating the room. Therefore, wherever in the privileged world there is light, there is physics!!

<span style="color: #404040; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">Finally, SAY CHEESE! Do you know that light that blinds you when your picture is taken? (Stupid flash) That’s an example of a rapid discharge of a capacitor. So next time, you are blinded at by your mom while taking prom pictures, curse at physics.



**<span style="color: #008080; font-family: Tahoma,Geneva,sans-serif; font-size: 110%;">Thanks for reading! We hope you managed to stuff some knowledge into your head. If you study up on this wiki ( and pay attention in class, I guess ) you are set for this part of physics. Congrats on making it all the way through the page, and thanks again **


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