Physics Book - User contributions [en]

Understanding Fundamentals of Current, Voltage, and Resistance

2025-09-21T06:42:45Z

Jsmith992: /* Quick Summary */

'''Ismail Elsissi (ielsissi3) Spring 2025'''

Circuitry are the building blocks of most electronics in our life. They are what keeps our computers running and our physics equipment functioning. Yet what exactly drives circuitry? The core components of a circuit revolves around three aspects: Current, Voltage, and Resistance.

The central concept in understanding the fundamentals of current, voltage, and resistance is unraveling the essential principles that govern the flow of electric charge. Current represents the rate of this flow of electrons through the circuit, represented by the symbol I and measured in Amperes. Voltage signifies the driving force behind it, or the pressure behind the source of the current. It is represented by the symbol V and measured in Volts. Resistance encapsulates the opposition encountered in the circuit, slowing and resisting the current. It is represented by the symbol R and measured in Ohms. A grasp of these fundamentals is crucial for navigating the intricacies of electrical systems and technology.

==Quick Summary==

{| class="wikitable"
! '''Concept''' || '''Equation / Definition''' || '''Notes''' || '''Units'''
|-
| Current (I) || <math>I = \frac{dQ}{dt}</math> || Flow of charge per unit time (in amperes) || <math>\frac{C}{s}</math>
|-
| Voltage (V) || <math>V = IR</math> || Electric potential difference (Ohm’s Law) || <math>\frac{J}{C}</math>
|-
| Resistance (R) || <math>R = \frac{V}{I}</math> || How much a component resists current flow || <math>\frac{J}{C^2s}</math>
|-
| Power (P) || <math>P = IV = I^2R = \frac{V^2}{R}</math> || Power dissipated or used by a resistor || <math>\frac{J}{s}</math>
|-
| Series Circuit || Same current through all; <math>R_\text{eq} = R_1 + R_2 + \cdots</math> || Voltage divides across resistors
|-
| Parallel Circuit || Same voltage across all; <math>\frac{1}{R_\text{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots</math> || Current divides across resistors
|-
| Kirchhoff’s Current Law (KCL) || Sum of currents into a junction = sum of currents out || Conservation of charge
|-
| Kirchhoff’s Voltage Law (KVL) || Sum of voltage changes in a loop = 0 || Conservation of energy
|}

==Ohm's Law==
[[Ohm's Law]], a fundamental principle in electrical engineering, establishes a foundational relationship between resistance, voltage, and current in a circuit. Named after the German physicist [[Georg Ohm]], the law states that the current passing through a conductor between two points is directly proportional to the voltage across the two points, given a constant temperature. Mathematically expressed as <math>{I = \frac{V}{R}}</math>, where I is the current in amperes, V is the voltage in volts, and R is the resistance in ohms, Ohm's Law is instrumental in unraveling the dynamic interplay between these three essential electrical parameters. This law provides a straightforward framework for understanding how changes in voltage or resistance influence the flow of current, and vice versa. Mastery of Ohm's Law is indispensable in analyzing and designing electrical circuits, serving as a cornerstone for engineers and enthusiasts as they navigate the intricate relationships among resistance, voltage, and current in the realm of electronics.

Understanding Ohm's law explains how our three components effect a circuit. <math>{I = \frac{V}{R}}</math>, the base component of our formula. The equation states Current is the Voltage divided by the Resistance. That is to say, the flow of electricity is equivalent to the driving force of the current divided by the opposition to the current. As we increase the voltage, or the driving force of the current, the current itself increases. On the other hand, if we increase the opposition to the current, the current decreases. As we examine these interactions we can see how the different components of the circuit affect each other.

[[File:OhmsTriangle.jpg]]
<br>''Image Source: Kenneth Jenkins''

==Computational Model==

View model here: https://trinket.io/embed/glowscript/922d8d312818

[[File:Glowscriptmodel-ezgif.com-crop.gif]]

Web VPython 3.2
from vpython import *

# Set up the scene
scene.title = "Visualization of Electric Currents with Graphs"
scene.width = 800
scene.height = 800
scene.background = color.black

# Create the first conductor (voltage increasing)
conductor1 = cylinder(pos=vector(-5, 1.5, 0), axis=vector(10, 0, 0), radius=0.2, color=color.gray(0.5))
arrow1 = arrow(pos=conductor1.pos + vector(0, conductor1.radius + 0.1, 0), axis=vector(0, 0, 0),
color=color.red, shaftwidth=0.1)
label1 = label(pos=arrow1.pos + vector(1.5, 0.5, 0), text="", color=color.white, height=12, box=False)

# Create the second conductor (resistance increasing)
conductor2 = cylinder(pos=vector(-5, 0, 0), axis=vector(10, 0, 0), radius=0.2, color=color.gray(0.5))
arrow2 = arrow(pos=conductor2.pos + vector(0, -conductor2.radius - 0.1, 0), axis=conductor2.axis,
color=color.green, shaftwidth=0.1)
label2 = label(pos=arrow2.pos + vector(1.5, -0.5, 0), text="", color=color.white, height=12, box=False)

# Create the third conductor (voltage and resistance increase at the same rate)
conductor3 = cylinder(pos=vector(-5, -1.5, 0), axis=vector(10, 0, 0), radius=0.2, color=color.gray(0.5))
arrow3 = arrow(pos=conductor3.pos + vector(0, -conductor3.radius - 0.1, 0), axis=vector(5, 0, 0), # Fixed length (half of cylinder)
color=color.blue, shaftwidth=0.1)
label3 = label(pos=arrow3.pos + vector(1.5, -0.5, 0), text="", color=color.white, height=12, box=False)

# Graph setup for Conductor 1
graph1 = graph(title="Voltage, Current, and Resistance (Conductor 1)", width=600, height=300,
xtitle="Time", ytitle="Value (scaled to 100)", foreground=color.white, background=color.black)
voltage_curve1 = gcurve(color=color.red, label="Voltage (V)")
current_curve1 = gcurve(color=color.green, label="Current (A)")
resistance_curve1 = gcurve(color=color.blue, label="Resistance (Ohms)")

# Graph setup for Conductor 2
graph2 = graph(title="Voltage, Current, and Resistance (Conductor 2)", width=600, height=300,
xtitle="Time", ytitle="Value (scaled to 100)", foreground=color.white, background=color.black)
voltage_curve2 = gcurve(color=color.red, label="Voltage (V)", graph=graph2)
current_curve2 = gcurve(color=color.green, label="Current (A)", graph=graph2)
resistance_curve2 = gcurve(color=color.blue, label="Resistance (Ohms)", graph=graph2)

# Graph setup for Conductor 3
graph3 = graph(title="Voltage, Current, and Resistance (Conductor 3)", width=600, height=300,
xtitle="Time", ytitle="Value (scaled to 100)", foreground=color.white, background=color.black)
voltage_curve3 = gcurve(color=color.red, label="Voltage (V)", graph=graph3)
current_curve3 = gcurve(color=color.green, label="Current (A)", graph=graph3)
resistance_curve3 = gcurve(color=color.blue, label="Resistance (Ohms)", graph=graph3)

# Initialize variables for Conductor 1
voltage1 = 0
max_voltage1 = 10
voltage_rate1 = 0.3 # Increased rate for voltage
resistance1 = 2
current1 = 0

# Initialize variables for Conductor 2
voltage2 = 10 # Constant voltage
resistance2 = 2 # Starts at 2
max_resistance2 = 10
resistance_rate2 = 0.1
current2 = 0

# Initialize variables for Conductor 3 (voltage and resistance increase at the same rate)
voltage3 = 1 # Start at 1 to avoid division by zero
resistance3 = 1 # Start at 1 for the same reason
voltage_rate3 = 0.1 # Same rate for voltage and resistance increase
resistance_rate3 = 0.1 # Same rate for resistance increase to maintain constant current
current3 = voltage3 / resistance3 # Initial current is V / R

# Particles for both conductors
particles1 = [sphere(pos=vector(4 - i, conductor1.pos.y + conductor1.radius, 0),
radius=0.05, color=color.blue, make_trail=True) for i in range(10)]
particles2 = [sphere(pos=vector(4 - i, conductor2.pos.y + conductor2.radius, 0),
radius=0.05, color=color.blue, make_trail=True) for i in range(10)]
particles3 = [sphere(pos=vector(4 - i, conductor3.pos.y + conductor3.radius, 0),
radius=0.05, color=color.blue, make_trail=True) for i in range(10)]

# Animate the currents and graphs
dt = 0.05
time = 0
while True:
rate(30)
time += dt

# Update Conductor 1 (Voltage Increasing)
if voltage1 < max_voltage1:
voltage1 += voltage_rate1 * dt
current1 = voltage1 / resistance1
arrow1.axis = vector(voltage1 * 0.4, 0, 0) # Arrow grows twice as fast
label1.text = f"Voltage: {voltage1:.1f} V\nCurrent: {current1:.2f} A"
voltage_curve1.plot(time, voltage1 * 10) # Scale voltage to graph's max height
current_curve1.plot(time, current1 * 10) # Scale current to graph's max height
resistance_curve1.plot(time, resistance1 * 10) # Scale resistance to graph's max height

# Update Conductor 2 (Resistance Increasing)
if resistance2 < max_resistance2:
resistance2 += resistance_rate2 * dt
current2 = voltage2 / resistance2 if resistance2 != 0 else 0
arrow2.axis = vector(conductor2.axis.x * (1 - resistance2 / max_resistance2), 0, 0) # Arrow shrinks
label2.text = f"Resistance: {resistance2:.1f} Ohms\nCurrent: {current2:.2f} A"
voltage_curve2.plot(time, voltage2 * 10) # Scale voltage to graph's max height
current_curve2.plot(time, current2 * 10) # Scale current to graph's max height
resistance_curve2.plot(time, resistance2 * 10) # Scale resistance to graph's max height

# Update Conductor 3 (Voltage and Resistance Increasing at the Same Rate)
voltage3 += voltage_rate3 * dt
resistance3 += resistance_rate3 * dt
current3 = voltage3 / resistance3 # Current stays constant as V and R increase at the same rate
arrow3.axis = vector(5, 0, 0) # Fixed length (half of cylinder length)
label3.text = f"Voltage: {voltage3:.1f} V\nResistance: {resistance3:.2f} Ohms\nCurrent: {current3:.2f} A"
voltage_curve3.plot(time, voltage3 * 10) # Scale voltage to graph's max height
current_curve3.plot(time, current3 * 10) # Scale current to graph's max height
resistance_curve3.plot(time, resistance3 * 10) # Scale resistance to graph's max height

# Animate particles for Conductor 1 (speed depends on current1)
speed1 = current1 * 0.5 # Adjust speed scaling factor if needed
for electron in particles1:
electron.pos.x -= speed1 * dt
if electron.pos.x < -5:
electron.pos.x = 5

# Animate particles for Conductor 2 (speed depends on current2)
speed2 = current2 * 0.5 # Adjust speed scaling factor if needed
for electron in particles2:
electron.pos.x -= speed2 * dt
if electron.pos.x < -5:
electron.pos.x = 5

# Animate particles for Conductor 3 (speed depends on current3)
speed3 = current3 * 0.5 # Adjust speed scaling factor if needed
for electron in particles3:
electron.pos.x -= speed3 * dt
if electron.pos.x < -5:
electron.pos.x = 5

==Current==
Current, in the realm of electrical circuits, refers to the flow of electric charge through a conductor. It is the rate at which electrons move along a closed path, commonly a wire or circuitry. Measured in amperes (A), current is a fundamental concept in understanding the dynamic behavior of electricity. The flow of electrons is driven by the electric potential difference, or voltage, which propels them from areas of higher potential to lower potential. Visualizing current involves picturing the movement of these charged particles, akin to a river of electrons streaming through the conductive pathways of a circuit. Whether in the context of powering household appliances or enabling complex electronic devices, a clear comprehension of current is pivotal for navigating the principles that underpin the functioning of electrical systems.
By convention, current is measured in the opposite direction of which electrons flow. This is likely because when current was first discovered, electrons had not yet been established in the scientific world. Hence, it could seem like positive charges were moving in a certain direction, rather than negative ones in the opposite as we know today. This convention still stands to this day, and in fact most likely makes calculations simpler, due to not having to account for the negative sign (-), which could cause for mistakes in calculations. However, it is certainly possible to solve a circuit problem with the opposite direction current, just with everything negated.

==Voltage==
Voltage, within the realm of electrical systems, is a measure of electric potential difference between two points in a circuit. It can be thought of as a change in electric potential, meaning that if there is no change, the voltage must be 0. Voltage does NOT measure anything at a given point, which is why a voltmeter must be connected at two different points in order to display a reading. These points should have some sort of change in current between them to be non-zero, such as the existence of a resistor or a node.
It represents the force that propels electric charges, typically electrons, to move through a conductor. Measured in volts (V), voltage serves as the driving factor behind the flow of current. It can be likened to the pressure in a water pipe that dictates the movement of water molecules; similarly, voltage dictates the movement of electric charges. Higher voltage implies a greater force pushing the charges, while lower voltage corresponds to a less forceful push. Understanding voltage is pivotal in comprehending the dynamics of electrical circuits, as it influences the rate and direction of the electric current, forming a foundational concept in the broader study of electrical engineering and technology.

==Resistance==
Resistance, in the realm of electrical systems, is the property that hinders the flow of electric current. It is a measure of the opposition encountered by the flow of electrons as they traverse through a conductor. This opposition leads to the conversion of electrical energy into heat. Resistance is quantified in ohms (Ω), and it is a critical factor in determining the behavior of circuits. Materials with high resistance impede the flow of current more strongly than those with low resistance. Resistors, specific components designed to introduce resistance intentionally, are commonly employed in circuits to regulate and control the flow of current, demonstrating the essential role that resistance plays in shaping the characteristics and functionality of electrical systems. This is because, when given the choice (such as a node splitting into two), current will try to flow through the wire with less resistance. This is why voltmeters are made with such high resistance - to avoid affecting the current flow (by having current flow through the voltmeter instead of the circuit), such an example why high resistance might be beneficial. A nuanced understanding of resistance is vital for engineers and enthusiasts alike as they design and optimize circuits for various applications.

==Examples==

===Simple===

'''Question 1'''

If a wire has 2 ohms of resistance and 3 volts of voltage, what is the current?

'''Answer'''

<math>{I = \frac{V}{R}}</math>

<math>{I = \frac{3}{2}}</math>

<math>{I = 1.5 \text{ Amps}}</math>

----
'''Question 2'''

If a wire has 6 ohms of resistance and 2 amperes of current, what is the voltage?

'''Answer'''

<math>{V = IR}</math>

<math>{V = 6*2}</math>

<math>{V = 12 \text{ Volts}}</math>

----

'''Question 3'''

If a wire has 18 ohms of resistance and 10 volts of voltage, what is the current?

'''Answer'''

<math>{R = \frac{I}{V}}</math>

<math>{R = \frac{18}{10}}</math>

<math>{R = 1.8 \text{ Ohms}}</math>

----

===Middling===

'''Question 4'''

A circuit has 2 3 volt batteries powering it. The circuit has 4 light bulbs, each providing 2 ohms of resistance. Assuming all components add up, what is the magnitude of the flow of the circuit?

'''Answer'''

<math>{V = 2*3 = 6}</math>

<math>{R = 4*2 = 8}</math>

<math>{I = \frac{6}{8} = 0.75 \text{ Amps}}</math>

----

===Difficult===

'''Question 5'''

A circuit has a constant current according to the total resistance, but the voltage drop is variable across each resistor according to its resistance and Ohm's law. A Circuit has a 10 volt battery at location 1, a 2 ohm resistor at location 2, a 3 ohm resistor at location 3, a 2 volt battery at location 4, a 5 ohm resistor at location 5, and a 6 ohm resistor at location 6 which connects back to the battery at location 1. What is the total current and the voltage drop at each location.

'''Answer'''

Current:
<math>{V_{total} = 10+2 = 12}</math>
<math>{R_{total} = 2+3+5+6 = 16}</math>
<math>{I_{total} = \frac{12}{16} = 0.75 Amps}</math>
Voltage Drops:

Resistor 1 (2 ohm): <math>{V = IR = 0.75 * 2 = 1.5 \text{ Volts}}</math>

Resistor 2 (3 ohm): <math>{V = IR = 0.75 * 3 = 2.25 \text{ Volts}}</math>

Resistor 3 (5 ohm): <math>{V = IR = 0.75 * 5 = 3.75 \text{ Volts}}</math>

Resistor 4 (6 ohm): <math>{V = IR = 0.75 * 6 = 4.5 \text{ Volts}}</math>

Checking answer (total voltage drop should be equivalent to total voltage provided, which as stated previously should be 12):

<math>{V = 1.5+2.25+3.75+4.5 = 12 \text{ Volts}}</math>

Correct! It is 12!

==Analogy to Water==

Circuitry can be conceptually likened to the flow of water through a network of pipes, providing an insightful analogy that simplifies the complex dynamics of electrical systems. In this analogy, electrical circuits serve as the conduits for the flow of electrons, analogous to water molecules coursing through pipes. The fundamental principles governing the behavior of both water and electrical circuits draw intriguing parallels, offering a relatable framework for understanding the intricate world of electronics.

Just as water moves from a source to various destinations through a network of interconnected pipes, electrical circuits facilitate the flow of electric current from a power source to multiple components within a system. The pipes themselves can be equated to conductive materials, such as copper wires, that guide the electrons along a predetermined path. Much like the pressure applied to water influencing its movement through pipes, voltage serves as the driving force behind the flow of electrons in a circuit.

Resistors within an electrical circuit find an analogy in the narrowing of pipes or the introduction of obstacles that impede the smooth passage of water. These resistive elements in a circuit limit the flow of electric current, generating heat in a manner akin to the friction-induced warmth observed in constricted water pipes. Capacitors and inductors, on the other hand, can be compared to the storage tanks and coiled sections in a water system, respectively. Capacitors store electrical energy, analogous to water reservoirs, while inductors store energy in a magnetic field, echoing the potential energy stored in coiled pipes.

The analogy of circuits as conduits for the flow of electrons, similar to water coursing through pipes, serves as a didactic tool, allowing individuals to grasp the intricacies of electrical systems through a familiar and tangible metaphor. Just as plumbing systems distribute water efficiently, electrical circuits enable the controlled movement of electrons, powering a myriad of devices and technologies that have become integral to our modern way of life.

===Examples of the Water/Pipe Analogy===

For a demonstration, please consider watching this video produced in collaboration with the EATON company.

<youtube>Z_s3TmYQAuc</youtube>

The electronics retailer Sparkfun also made a video in similar format to EATON's, covering the topics in a much more in depth way.

<youtube>8jB6hDUqN0Y</youtube>

==Connectedness to Applications Outside of Physics==
The concepts encapsulated in Ohm's Law transcend the confines of physics, resonating profoundly in the realm of engineering and various practical applications. Engineering disciplines, particularly electrical and electronic engineering, heavily rely on the principles outlined in Ohm's Law to design, analyze, and optimize a myriad of systems and devices. Understanding the interplay between resistance, voltage, and current allows engineers to predict and control the behavior of electrical circuits, ensuring the efficient and safe operation of electronic components.

In the field of electrical engineering, Ohm's Law is a cornerstone for designing circuits with specific performance characteristics. Engineers leverage the law to determine the appropriate resistances needed for components, calculate voltage drops across various elements, and establish the current requirements for optimal functionality. Whether designing intricate integrated circuits or power distribution systems, the principles of Ohm's Law provide a fundamental framework for engineers to achieve desired electrical outcomes.

Beyond traditional engineering disciplines, Ohm's Law finds application in diverse technological domains. For instance, in the burgeoning field of renewable energy, such as solar power systems, understanding the relationship between voltage, current, and resistance is crucial for designing efficient energy conversion and storage systems. Similarly, in telecommunications, where signal integrity is paramount, the principles of Ohm's Law guide the design of communication networks, ensuring reliable transmission of information through cables and electronic components.

In essence, the universality of Ohm's Law extends its influence into a spectrum of engineering applications, shaping the way professionals approach challenges in fields ranging from electronics and telecommunications to renewable energy. Its principles serve as a practical and indispensable tool, providing a systematic approach to understanding and manipulating the behavior of electrical systems in the pursuit of technological innovation.

==Initial vs Steady State==
A critical difference in steady state vs. initial state circuits is how capacitors behave. Initially they are uncharged, and so charge will flow to them to be stored. At steady state, the capacitor is fully charged and the current there is zero. Therefore, if there is a loop with a capacitor, it can be treated as "open" (essentially as if the wire were not connected there, and loop rules as such would apply.

==History==
In the early 19th century, the study of electricity was in its infancy, and it was during this time that German physicist [https://www.physicsbook.gatech.edu/Georg_Ohm Georg Simon Ohm] made groundbreaking contributions, laying the foundation for what would become Ohm's Law. Ohm, born in Erlangen, Bavaria, in 1789, embarked on his scientific journey in an era marked by fervent exploration into the nature of electricity.

Georg Simon Ohm's pioneering work culminated in 1827 when he published his seminal treatise "Die galvanische Kette, mathematisch bearbeitet" ("The Galvanic Circuit Investigated Mathematically"). In this work, Ohm unveiled the relationship between voltage, current, and resistance, providing a mathematical formula that encapsulated the fundamental principles. His revolutionary concept, known today as Ohm's Law, asserted that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to the resistance it offers.

Ohm's Law addressed a pressing need in the scientific community at the time, offering a quantitative framework to comprehend and manipulate electrical circuits. It was a watershed moment that transformed electricity from a mysterious force into a quantifiable and predictable phenomenon.

The practical implications of Ohm's Law began to unfold as the fields of physics and engineering evolved. Michael Faraday's groundbreaking work in electromagnetic induction in the early 19th century and James Clerk Maxwell's formulation of Maxwell's Equations in the mid-19th century further enriched the understanding of electricity, providing context to Ohm's Law.

As electrical science progressed, so did the understanding of voltage, current, and resistance. The introduction of the telegraph in the mid-19th century and the subsequent development of electrical power distribution systems in the late 19th century underscored the practical utility of these concepts. Engineers and scientists across the globe, including luminaries like Thomas Edison and Nikola Tesla, applied the principles elucidated by Ohm to propel the electrical revolution, shaping the modern technological landscape.

In summary, Ohm's Law emerged as a cornerstone in the historical tapestry of electrical science, catalyzing a transformative shift in how electricity was understood and harnessed. Its profound impact resonates through centuries, influencing the trajectory of technological progress and laying the groundwork for the sophisticated electrical systems that define our contemporary world.

== See also ==
<youtube>mc979OhitAg&list=PLWv9VM947MKi_7yJ0_FCfzTBXpQU-Qd3K‎</youtube>

===Further reading===
Access to IEEE Xplore (a digital library covering all aspects of Electrical and Computer Engineering) is provided for free through the Georgia Tech Library. The library offers various free ebooks covering topics of [https://ieeexplore.ieee.org/book/5521805 Power Systems], and [https://ieeexplore.ieee.org/book/9549029 Electricity and Electronics Fundamentals].

==References==
#[https://www.fluke.com/en-us/learn/blog/electrical/what-is-ohms-law What is Ohm’s Law? (n.d.). Fluke LLC.]

[[Category:Circuits]]

Main Page

2025-09-21T06:32:23Z

Jsmith992: /* Kirchoff's Laws */

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</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Iterative Prediction]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">

====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">

*[[Kinematics]]
*[[Projectile Motion]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Fundamentals of Iterative Prediction with Varying Force]]
*[[Spring_Force]]
*[[Simple Harmonic Motion]]


*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Predicting Change in multiple dimensions]]
*[[Two Dimensional Harmonic Motion]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">
*[[Gravitational Force]]
*[[Gravitational Force Near Earth]]
*[[Gravitational Force in Space and Other Applications]]
*[[3 or More Body Interactions]]

*[[Electric Force]]
*[[Introduction to Magnetic Force]]
*[[Strong and Weak Force]]
*[[Reciprocity]]
*[[Conservation of Momentum]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Properties of Matter====
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young's Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Change of State]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
====Isabel Hollhumer F24====
*[[Free Body Diagram]]
*[[Inclined Plane]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Curving Motion====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Jeet Bhatkar====

====Energy Principle====
The Energy Principle is a fundamental concept in physics that describes the relationship between different forms of energy and their conservation within a system. Understanding the Energy Principle is crucial for analyzing the motion and interactions of objects in various physical scenarios.
<div class="mw-collapsible-content">

*[[Kinetic Energy]]
Kinetic energy is the energy an object possesses due to its motion.
*[[Work/Energy]]
Potential energy arises from the position of an object relative to its surroundings. Common forms of potential energy include gravitational potential energy and elastic potential energy.
*[[The Energy Principle]]
Work and energy are closely related concepts. Work (
𝑊) done on an object is defined as the force (
𝐹) applied to the object multiplied by the displacement (
𝑑) of the object in the direction of the force:
The Energy Principle states that the total mechanical energy of a system remains constant if only conservative forces (forces that depend only on the positions of the objects) are acting on the system.
*[[Conservation of Energy]]
The principle of conservation of energy states that the total energy of an isolated system remains constant over time. In other words, energy cannot be created or destroyed, only transformed from one form to another. This principle is a fundamental concept in physics and has wide-ranging applications in mechanics, thermodynamics, and other branches of science.
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Work by Non-Constant Forces====
<div class="mw-collapsible-content">
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential Energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
*[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Choice of System====
<div class="mw-collapsible-content">
*[[System & Surroundings]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Thermal Energy, Dissipation, and Transfer of Energy====
<div class="mw-collapsible-content">
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Calorific Value(Heat of combustion)]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
*[[The Third Law of Thermodynamics]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
*[[Rolling Motion]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
*[[Kinetic Friction]]
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====Conservation of Momentum====
<div class="mw-collapsible-content">
*[[Conservation of Momentum]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Collisions====
<div class="mw-collapsible-content">
*[[Newton's Third Law of Motion]]
*[[Collisions]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotational Kinematics]]
*[[Eulerian Angles]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Angular Momentum====
<div class="mw-collapsible-content">
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[The Moments of Inertia]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Analyzing Motion with and without Torque====
<div class="mw-collapsible-content">
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Introduction to Quantum Concepts====
<div class="mw-collapsible-content">
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
*[[Electron transitions]]
*[[Entropy]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====

<div class="mw-collapsible-content">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Field and Electric Potential]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric force====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Conductors and Insulators====
<div class="mw-collapsible-content">
*[[Conductivity and Resistivity]]
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Conductors]]
*[[Polarization of a conductor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Charging and Discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Field of a Charged Rod|Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of a Potential Difference]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges, electron current, and conventional current====

<div class="mw-collapsible-content">
*[[Moving Point Charge]]

A moving point charge creates both electric and magnetic fields. As the charge accelerates or changes position, it alters the surrounding electromagnetic field, which can influence other charges nearby. This is the fundamental concept behind electromagnetic radiation and wave propagation. When many charges move collectively—such as electrons in a wire—this flow is referred to as electric current. This perfectly segues us into the next section of this page.

*[[Current]]

Current is typically measured in amperes and represents the rate at which charge flows through a surface. Although electrons carry the charge and move from negative to positive, conventional current is defined in the opposite direction: from positive to negative. This convention dates back to early scientific assumptions and remains standard in circuit diagrams and equations today.

</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
*[[Magnetic Field of a Curved Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a Charged Disk====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Disk]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">

====Circuitry Basics====
<div class="mw-collapsible-content">
*[[Understanding Fundamentals of Current, Voltage, and Resistance]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Kirchoff's Laws====
<div class="mw-collapsible-content">
*[[Loop Rule]]
*[[Node Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Electric Potential Difference]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
*[[Fundamentals of Resistance]]
*[[Problem Solving]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
*[[AC and DC]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Motors and Generators]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[VPython Modelling of Electric and Magnetic Forces]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>

====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
*[[Current in an RL Circuit]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
==== Electromagnetic Radiation ====
<div class="mw-collapsible-content">
*[[Electromagnetic Radiation]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
*[[Classical Physics]]
</div>
</div>

[[Category:Which Category did you place this in?]]

===Weeks 2 and 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity and the Lorentz Transformation====
<div class="mw-collapsible-content">
*[[Frame of Reference]]

*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Twin Paradox]]
*[[Lorentz Transformations]]
*[[Relativistic Doppler Effect]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons and the Photoelectric Effect====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
*[[The Photoelectric Effect]]
</div>
</div>

===Weeks 5 and 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves and Wave-Particle Duality====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
*[[Particle in a 1-Dimensional box]]
*[[Heisenberg Uncertainty Principle]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
*[[Fourier Series and Transform]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Schrödinger Equation====
<div class="mw-collapsible-content">
*[[The Born Rule]]
*[[Solution for a Single Free Particle]]
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]
*[[Quantum Harmonic Oscillator]]
*[[Solution for Simple Harmonic Oscillator]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Quantum Mechanics====
<div class="mw-collapsible-content">
*[[Quantum Tunneling through Potential Barriers]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
*[[Nucleus]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
*[[Molecules]]
*[[Covalent Bonds]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
*[[Application of Statistics in Physics]]
</div>
</div>

===Week 15===
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====Statistical Physics====
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*[[Temperature & Entropy]]
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===Additional Topics===
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====Thermodynamics====
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*[[Maxwell Relations]]
*[[Brownian Motion]]
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====Nuclear Physics====
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*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
*[[Radioactive Decay Processes]]
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====Particle Physics====
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*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
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====Solid-State/Condensed Matter Physics====
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*[[What is Condensed Matter]]
*[[Crystalline Structures]]
*[[Electric-Band Structure]]
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