BackCapacitance and Capacitor Circuits: Study Notes for PHY 131
Study Guide - Smart Notes
Tailored notes based on your materials, expanded with key definitions, examples, and context.
Capacitance and Capacitors
Introduction to Capacitance
Capacitance is a fundamental concept in electricity and magnetism, describing the ability of a system to store electric charge. It is a key topic in university-level physics courses, particularly in the study of electric circuits.
Definition: Capacitance (C) is defined as the ratio of the magnitude of charge (Q) stored on one plate of a capacitor to the potential difference (V) between the plates.
Unit: The SI unit of capacitance is the farad (F), where 1 F = 1 C/V.
Physical Meaning: Capacitance measures how much charge a capacitor can store for a given voltage.
Types of Capacitors
Capacitors come in various geometries, each with distinct properties and applications. The most common types are parallel-plate and cylindrical capacitors.
Parallel-Plate Capacitor: Consists of two conductive plates separated by an insulating material (dielectric).
Cylindrical Capacitor: Formed by two coaxial cylinders, often used in cable and transmission line applications.
Formulas:
Parallel-Plate Capacitor:
A: Area of one plate
d: Separation between plates
: Permittivity of free space
Cylindrical Capacitor:
L: Length of cylinders
a: Radius of inner cylinder
b: Radius of outer cylinder
Capacitors in Circuits
Circuit Symbols
Understanding circuit diagrams requires familiarity with standard symbols for capacitors, batteries, and switches.
Capacitor: Two parallel lines
Battery: Alternating long and short lines
Switch: Break in a line with a movable contact
Capacitors in Series
When capacitors are connected in series, the total capacitance is less than any individual capacitance. The same charge passes through each capacitor, but the voltage divides among them.
Formula for Series Connection:
Key Point: The equivalent capacitance is always less than the smallest individual capacitance in the series.
Capacitors in Parallel
In parallel, capacitors share the same voltage, and the total capacitance is the sum of individual capacitances.
Formula for Parallel Connection:
Key Point: The equivalent capacitance is always greater than any individual capacitance in the parallel arrangement.
Capacitor Circuits: Example Calculations
Capacitor circuits often require calculating equivalent capacitance for combinations of series and parallel connections.
Example: For two capacitors, and in series:
Example: For the same capacitors in parallel:
Energy Stored in a Capacitor
Energy Storage
Capacitors store energy in the electric field between their plates. This energy can be calculated using the following formula:
Energy Stored:
U: Energy stored (in joules)
C: Capacitance (in farads)
V: Voltage across the capacitor (in volts)
Energy Density: The energy density (energy per unit volume) in the electric field is:
E: Electric field strength
Applications
Capacitors are used in electronic circuits for energy storage, filtering, and timing applications.
Energy storage in capacitors is crucial in devices like camera flashes and defibrillators.
Summary Table: Series vs. Parallel Capacitor Connections
Connection Type | Formula for | Voltage Across Each Capacitor | Charge on Each Capacitor |
|---|---|---|---|
Series | Divides among capacitors | Same for all capacitors | |
Parallel | Same across all capacitors | Divides among capacitors |
Additional info: These notes expand upon the brief points in the slides, providing full definitions, formulas, and context for college-level physics students studying electricity and magnetism.
