#AP Physics 2: Resistance and Capacitance - The Ultimate Study Guide ⚡

Hey there, future AP Physics 2 master! Let's get you prepped and confident for your exam. This guide is designed to be your go-to resource, especially the night before the test. We'll break down complex topics into easy-to-digest concepts, so you can walk into that exam feeling like a total pro. Let's dive in!

#Capacitance: Storing Energy in Electric Fields 🔋

#What's a Capacitor?

A capacitor is a device that stores electrical charge and energy in an electric field. Think of it like a tiny rechargeable battery, but instead of chemical reactions, it uses electric fields to store energy. Capacitors are essential in many electronic devices, from camera flashes to computer circuits.

Key Idea: A capacitor consists of two conductive plates separated by an insulator (dielectric). When a voltage is applied, charge accumulates on the plates, creating an electric field between them.

Key Concept

Capacitors store charge and energy. The ability to store charge is called capacitance (C).

A typical parallel-plate capacitor.

#Parallel Plate Capacitor: The Basics

The simplest capacitor is the parallel-plate capacitor, which consists of two conductive plates separated by a small distance. When connected to a battery, charge accumulates on the plates, creating an electric field. The amount of charge a capacitor can store is proportional to the voltage applied.

Charge and Voltage: The relationship between charge (Q) and voltage (V) is given by: $Q = CV$ , where C is the capacitance.
Capacitance (C): The ability of a capacitor to store charge. Measured in Farads (F), where 1 F = 1 C/V.

Memory Aid

Q = CV: "Queen (Q) = Cat (C) Very (V)".

A capacitor being charged by a battery.

#Deriving Capacitance

The capacitance of a parallel-plate capacitor can be derived from its physical dimensions:

$C = \frac{ϵ_0 A}{d}$

Where:

C is capacitance
ε₀ is the permittivity of free space ( $8.85 \times 10^{-12} F/m$ )
A is the area of the plates
d is the distance between the plates

Quick Fact

Capacitance is directly proportional to the area of the plates and inversely proportional to the distance between them.

#Energy Stored in a Capacitor

Capacitors store energy in the electric field between their plates. The energy stored (U) can be calculated using the following formulas:

$U = \frac{1}{2}CV^2 = \frac{1}{2}\frac{Q^2}{C} = \frac{1}{2}QV$

Key Idea: Energy is stored in the electric field, not just on the plates themselves.

Exam Tip

Remember all three forms of the energy equation. They are all on the equation sheet but knowing them will save you time.

#Practice Questions 👍

Practice Question

A 20 µF parallel-plate capacitor is fully charged to 20 V. The energy stored in the capacitor is most nearly __________.
- (A) 2 mJ
- (B) 4 mJ
- (C) 20 mJ
- (D) 40 mJ
Answer: (B) 4 mJ

#AP Physics 2: Resistance and Capacitance - The Ultimate Study Guide ⚡

#Capacitance: Storing Energy in Electric Fields 🔋

#What's a Capacitor?

Key Idea: A capacitor consists of two conductive plates separated by an insulator (dielectric). When a voltage is applied, charge accumulates on the plates, creating an electric field between them.

Key Concept

Capacitors store charge and energy. The ability to store charge is called capacitance (C).

A typical parallel-plate capacitor.

#Parallel Plate Capacitor: The Basics

Charge and Voltage: The relationship between charge (Q) and voltage (V) is given by: $Q = CV$ , where C is the capacitance.
Capacitance (C): The ability of a capacitor to store charge. Measured in Farads (F), where 1 F = 1 C/V.

Memory Aid

Q = CV: "Queen (Q) = Cat (C) Very (V)".

A capacitor being charged by a battery.

#Deriving Capacitance

The capacitance of a parallel-plate capacitor can be derived from its physical dimensions:

$C = \frac{ϵ_0 A}{d}$

Where:

C is capacitance
ε₀ is the permittivity of free space ( $8.85 \times 10^{-12} F/m$ )
A is the area of the plates
d is the distance between the plates

Quick Fact

Capacitance is directly proportional to the area of the plates and inversely proportional to the distance between them.

#Energy Stored in a Capacitor

Capacitors store energy in the electric field between their plates. The energy stored (U) can be calculated using the following formulas:

$U = \frac{1}{2}CV^2 = \frac{1}{2}\frac{Q^2}{C} = \frac{1}{2}QV$

Key Idea: Energy is stored in the electric field, not just on the plates themselves.

Exam Tip

Remember all three forms of the energy equation. They are all on the equation sheet but knowing them will save you time.

#Practice Questions 👍

Practice Question

A 20 µF parallel-plate capacitor is fully charged to 20 V. The energy stored in the capacitor is most nearly __________.
- (A) 2 mJ
- (B) 4 mJ
- (C) 20 mJ
- (D) 40 mJ
Answer: (B) 4 mJ

Resistance and Capacitance

Owen Perez

#AP Physics 2: Resistance and Capacitance - The Ultimate Study Guide ⚡

#Capacitance: Storing Energy in Electric Fields 🔋

#What's a Capacitor?

#Parallel Plate Capacitor: The Basics

#Deriving Capacitance

#Energy Stored in a Capacitor

#Practice Questions 👍

How are we doing?

Resistance and Capacitance

Owen Perez

#AP Physics 2: Resistance and Capacitance - The Ultimate Study Guide ⚡

#Capacitance: Storing Energy in Electric Fields 🔋

#What's a Capacitor?

#Parallel Plate Capacitor: The Basics

#Deriving Capacitance

#Energy Stored in a Capacitor

#Practice Questions 👍

How are we doing?