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Unit 3

3.1 Unit 3: Electric Circuits

4 min readโ€ขnovember 3, 2020

peter57616

Peter Apps


3.0: Overview ๐ŸŒ

Unit 3 is all about connecting electrical devices together. We'll look at different types of circuits, how to calculate the flow of electricity through a circuit, and do some analysis of the current, power, and potential difference in various locations in a circuit.
This unit makes up 17-23% of the AP exam and will take 13-26 days to cover depending on class length. The Unit 3 personal progress checkpoint on AP Classroom has around 35 multiple choice questions and 1 free response question for you to practice and check your understanding with.

3.1: Circuit Quantities ๐Ÿ”‹

In Unit 1, we studied voltage and defined it as work per unit charge. There are 2 other important quantities used along with voltage to describe the features of a circuit: current and resistance.
A common analogy for how voltage, current, and resistance are related to each other is to think of an electric circuit like water flowing through a hose. Voltage is similar to the water pressure, current is similar to the amount of water that gets through the hose, and resistance is similar to mud or dirt that gets stuck in the hose and starts to clog it.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-nN5O73b7DMD4.png?alt=media&token=8b1ff236-b58a-4855-b9f9-662737d3c298

Image from freeingenergy.com

Current ๐Ÿ’จ

Current is defined as the rate at which charge flows through a circuit. It's represented by the equation:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-P8ExinC8LvcZ.png?alt=media&token=c3eb4a0b-ac32-49f3-bf66-653efb6b2a25
where I is the current (measured in Amps or milliAmps), Q is the charge passing a given point, and t is the time for the charge to pass through that point.
Conventional Current is defined as the direction a positive charge carrier will travel. This may seem strange to us since chemistry tells us that the electrons are the mobile part of the atom. Nevertheless, there are several advantages to choosing a positive direction, since that aligns with our choices in direction when it comes to electric fields and potential differences (see Unit 1).
On a microscopic level, current is also related to the drift velocity (v_d) of the individual charge carriers. Drift velocity can be thought of as the average velocity of each charge carrier as it moves through a wire. In the image below, we're looking at the path of the electron as it moves through a wire.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-cJXaq7yNBJrY.jpg?alt=media&token=74f12c22-260f-4338-beab-fc4227632e9a

Image from openstax.org

We can imagine that the current in the wire would depend on the total number of charge carriers moving through the wire as well. A larger diameter wire would allow for more carriers. Combining these ideas together we can derive an equation for current.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-hmil7QgY333E.png?alt=media&token=99f53c25-eb69-4776-9af1-fb72247476ba

Image from hyperphysics

Current Density is a third way of describing the current in terms of the electric field, E, and the material it is traveling through. In this case, we define current density as a vector, \vec{J} . We then relate the electric field to the current density through the equation below. (For a full derivation of this equation, check out this link)
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-MNQscC4DuMXF.png?alt=media&token=bb71404a-9e8b-493b-9aef-116647226d82
p is the proportionality constant between E and J and is called the resistivity. Resistivity describes how much a given material restricts the current. Resistivity depends on temperature (higher temperatures result in a higher resistivity, but most tables give values for 20 C)
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-JmWRNMINlB2t.png?alt=media&token=28c3ae70-5578-497c-9db3-1e293c9101d9

Data from NYS Physics Reference Tables

Resistance ๐Ÿ›‘

While resistivity describes how much a material restricts the current, resistance (R) is much more useful for describing a circuit. It takes into account the length (L) and cross-sectional area (A) of the conductor as well.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-1svRjESWx1ZQ.png?alt=media&token=52ab9a64-a3af-4e40-817e-499a4f104922
Resistance is defined as the opposition to current and can be a very useful feature when trying to design a circuit. For example, if the current gets too high in a cell phone, the battery starts expanding and can catch fire or explode. However, there are also times where you want to keep the resistance as low as possible (such as transmitting electricity from a power plant to people's homes). Resistance is measured in Ohms(ฮฉ), where
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-qHozAc6up9E3.png?alt=media&token=b8231e32-08cc-4f5a-87e2-da54fea68d64

Ohm's Law ๐Ÿ’ก

The basic mathematical relationship between resistance and current is defined by Ohm's Law. Depending on your context, it's written one of 3 ways. It doesn't actually matter which one you're more familiar with since they're all the same equation.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-76Uo3iLGNg2D.png?alt=media&token=60d034dc-9e72-4432-a863-55b554e85b3d
This law relates our three main circuit quantities in a nice simple equation. You will often see this represented in graphical form and be asked to infer if the device is Ohmic or non-Ohmic. As you can see in the graph below, an Ohmic device has a constant linear slope, while a non-Ohmic device does not. Sometimes a device can have an Ohmic region, then become non-ohmic.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-0nzc5TAPZtbc.png?alt=media&token=434d497a-07cd-4f82-9d35-01617e681279

Image from www.menihek.ca/

Practice Question

  1. https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-6V0lCULCO0Pw.png?alt=media&token=1e32f8f9-abe2-4dad-84e4-8ae7f140f137

Image from AP Classroom

Answer

Choice B is correct. Because the resistance of a wire depends on
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-B4GgHyyrTGVk.png?alt=media&token=73a6fb9e-5d34-47ed-a1e7-bfa9030ceade
, a longer length and smaller area will result in the greatest resistance

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