College Physics: Capacitors and Dielectrics
Chapter 19 Electric Potential and Electric Field
19.5 Capacitors and Dielectrics
Definition of a Capacitor
A capacitor is a device used to store electric charge.
It has various applications, such as:
Filtering static in radio reception
Energy storage in heart defibrillators
Capacitors typically consist of
Two conducting plates close together but not in contact, with an insulator (dielectric) between them.
Function of Capacitors
When connected to battery terminals:
An initially uncharged capacitor experiences separation of charges, with positive charge (+Q) on one plate and negative charge (-Q) on the other.
Despite the separation, the capacitor remains neutral overall.
Factors Affecting Charge Storage
The amount of charge a capacitor can store depends on:
The applied voltage (
The physical characteristics of the capacitor, primarily its size (plate area and distance between plates).
Parallel Plate Capacitors
A parallel plate capacitor consists of
Two identical conducting plates separated by a distance.
The relationship between voltage and stored charge is defined as:
E ext{ (Electric Field Strength)} ext{ is proportional to the charge (Q) and voltage (V)}.
E ext{ is proportional to } \frac{Q}{A} \text{ where A is the area of the plates}
The equation governing capacitance (C) is:
C = \frac{Q}{V}
Units of capacitance: The unit of capacitance is the farad (F).
Capacitance Calculation Principles
The capacitance of a parallel plate capacitor can be derived from physical characteristics:
C = \frac{\epsilon_0 A}{d}
where:
\epsilon_0 = Permittivity of free space (8.85 × 10^(-12) F/m)
A = area of one plate (in square meters)
d = distance between the plates (in meters)
A 1-farad capacitor will store 1 coulomb of charge with 1 volt applied.
Typical capacitor values range from picofarads (pF) to millifarads (mF).
Dielectrics and Their Role
Dielectrics are insulating materials used between plates of a capacitor to:
Increase Capacitance: A dielectric increases capacitance by reducing the electric field within the capacitor, allowing it to store more charge at a given voltage.
Allow Greater Voltage: Dielectrics can withstand higher voltage before breakdown occurs, thus increasing the operational capacity of the capacitor.
The equation for capacitance with a dielectric factor (κ) is:
C = κC0 where C0 is the capacitance without dielectric.
The dielectric constant (κ) is a property of the material and influences how much capacitance increases.
Characteristics of Dielectric Materials
Dielectric constants for various materials:
Material
Dielectric Constant
Vacuum
1.00000
Air
1.00059
Water
80
Teflon
2.1
Dielectric Strength: The maximum electric field strength at which a dielectric begins to conduct. Example values:
Air: ~3 × 10^6 V/m
Teflon: ~60 × 10^6 V/m
Practical Example of Capacitance Calculation
Example 1: Finding Capacitance and Charge Stored
(a) Given: Parallel plate capacitor with plates of area A = 1.00 m², separation d = 1.00 mm; applied voltage = 3000 V.
The capacitance is calculated as follows:
C = \frac{\epsilon_0 A}{d} = \frac{(8.85 × 10^{-12} F/m)(1.00 m²)}{0.001 m} = 8.85 × 10^{-9} F = 8.85 nF
(b) The charge can then be computed using:
Q = CV = (8.85 × 10^{-9} F)(3000 V) = 26.55 μC
Biological Application of Capacitors
The cell's plasma membrane behaves similarly to a capacitor, maintaining a potential difference of about -70 mV.
This membrane allows for the selective passage of ions, with a predominant concentration of positively charged sodium ions (Na+) outside and negatively charged ions inside.
Conclusion
Capacitors play crucial roles in various electronic appliances and biological systems; they store and regulate electrical energy efficiently through controlled charge migration, supported by insulators (dielectrics) that enhance performance and safety while handling voltages.