This study guide covers inductors and their behavior in circuits. Key topics include: inductance (L) and its dependence on coil geometry, energy storage in inductors, LR circuit behavior (including the time constant), LC circuit oscillations (and their connection to simple harmonic motion), and relevant circuit analysis techniques. It also includes practice problems and exam tips.

#AP Physics C: E&M - Inductors: The Ultimate Study Guide ⚡

Hey there, future physicist! Let's dive into inductors and circuits, making sure you're totally prepped for the AP exam. This guide is designed to be your go-to resource, especially the night before the test. Let's make this click!

#What is an Inductor? 🤔

An inductor is essentially a coil of wire, often wrapped around a core, that resists changes in current. Think of it as a current smoother. It stores energy in a magnetic field, kind of like how a capacitor stores energy in an electric field. 💡

Image from wikipedia.org - Various types of inductors

We define inductance (L) as the proportionality constant between magnetic flux and current:

$\Phi_B = LI$

Where:

$\Phi_B$ is the magnetic flux
L is the inductance (measured in Henries (H))
I is the current

Key Concept

Inductance L depends on the coil's geometry (number of loops, wire gauge) and the core material. More loops = more inductance! A larger core also increases inductance.

Applying Faraday's Law, we find the induced EMF in an inductor:

$\varepsilon = -L \frac{dI}{dt}$

This induced EMF opposes any change in current. It's like the inductor is saying, "Hey, hold on! Don't change the current so fast!" This is Lenz's Law in action.

#Energy Stored in an Inductor 🔋

Consider a simple circuit with a battery, resistor, and inductor:

When the switch closes, current flows, and the inductor stores energy in its magnetic field. Using Kirchhoff's Voltage Law, we can derive the energy stored:

$U = \frac{1}{2}LI^2$

Quick Fact

This formula is analogous to the energy stored in a capacitor ( $\frac{1}{2}CV^2$ ). Inductors store energy in the magnetic field, capacitors in the electric field.

#LR Circuit Behavior 🔍

Now, let's look at the current and voltage behavior in a circuit with both a resistor and an inductor (LR circuit):

<img src="https://zupay.blob.core.windows.net/resources/files/0baca4f69800419293b4c75aa2870acd_26ae87_3907.png?alt=media&token=bb259369-d71f-46b5-b47f-e4a951...

#AP Physics C: E&M - Inductors: The Ultimate Study Guide ⚡

#What is an Inductor? 🤔

Image from wikipedia.org - Various types of inductors

We define inductance (L) as the proportionality constant between magnetic flux and current:

$\Phi_B = LI$

Where:

$\Phi_B$ is the magnetic flux
L is the inductance (measured in Henries (H))
I is the current

Key Concept

Inductance L depends on the coil's geometry (number of loops, wire gauge) and the core material. More loops = more inductance! A larger core also increases inductance.

Applying Faraday's Law, we find the induced EMF in an inductor:

$\varepsilon = -L \frac{dI}{dt}$

This induced EMF opposes any change in current. It's like the inductor is saying, "Hey, hold on! Don't change the current so fast!" This is Lenz's Law in action.

#Energy Stored in an Inductor 🔋

Consider a simple circuit with a battery, resistor, and inductor:

When the switch closes, current flows, and the inductor stores energy in its magnetic field. Using Kirchhoff's Voltage Law, we can derive the energy stored:

$U = \frac{1}{2}LI^2$

Quick Fact

This formula is analogous to the energy stored in a capacitor ( $\frac{1}{2}CV^2$ ). Inductors store energy in the magnetic field, capacitors in the electric field.

#LR Circuit Behavior 🔍

Now, let's look at the current and voltage behavior in a circuit with both a resistor and an inductor (LR circuit):

<img src="https://zupay.blob.core.windows.net/resources/files/0baca4f69800419293b4c75aa2870acd_26ae87_3907.png?alt=media&token=bb259369-d71f-46b5-b47f-e4a951...

What is the primary function of an inductor in an electrical circuit? 🤔

To act as a perfect conductor, allowing current to flow unimpeded

To store energy in an electric field

To resist changes in current and store energy in a magnetic field

To dissipate energy in the form of heat

What is the primary function of an inductor in an electrical circuit? 🤔

To act as a perfect conductor, allowing current to flow unimpeded

To store energy in an electric field

To resist changes in current and store energy in a magnetic field

To dissipate energy in the form of heat

Inductance

Samuel Young

#AP Physics C: E&M - Inductors: The Ultimate Study Guide ⚡

#What is an Inductor? 🤔

#Energy Stored in an Inductor 🔋

#LR Circuit Behavior 🔍

How are we doing?

Inductance

Samuel Young

#AP Physics C: E&M - Inductors: The Ultimate Study Guide ⚡

#What is an Inductor? 🤔

#Energy Stored in an Inductor 🔋

#LR Circuit Behavior 🔍

How are we doing?