#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

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:

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

#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...