Physics 2102 Lecture 7 - PowerPoint PPT Presentation

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Physics 2102 Lecture 7

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Physics 2102 Jonathan Dowling Physics 2102 Lecture 7 Capacitors I Capacitors and Capacitance Capacitor: any two conductors, one with charge +Q, other with charge Q ... – PowerPoint PPT presentation

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Title: Physics 2102 Lecture 7


1
Physics 2102 Lecture 7
  • Capacitors I

2
Capacitors and Capacitance
  • Capacitor any two conductors, one with charge
    Q, other with charge Q

Q
Potential DIFFERENCE between conductors V
Q
Uses storing and releasing electric
charge/energy. Most electronic
capacitors micro-Farads (mF), pico-Farads (pF)
1012 F New technology compact 1 F capacitors
Q CV where C capacitance
Units of capacitance Farad (F) Coulomb/Volt
3
Capacitance
  • Capacitance depends only on GEOMETRICAL factors
    and on the MATERIAL that separates the two
    conductors
  • e.g. Area of conductors, separation, whether the
    space in between is filled with air, plastic,
    etc.

(We first focus on capacitors where gap is filled
by AIR!)
4
Electrolytic (1940-70) Electrolytic (new)
Paper (1940-70)
Capacitors
Variable air, mica
Mica (1930-50)
Ceramic (1930 on)
Tantalum (1980 on)
5
Parallel Plate Capacitor
We want capacitance CQ/V
Area of each plate A Separation d charge/area
s Q/A
E field between the plates (Gauss Law)
Relate E to potential difference V
Q
-Q
What is the capacitance C ?
6
Capacitance and Your iPod!
7
Parallel Plate Capacitor Example
  • A huge parallel plate capacitor consists of two
    square metal plates of side 50 cm, separated by
    an air gap of 1 mm
  • What is the capacitance?

C e0A/d (8.85 x 1012 F/m)(0.25 m2)/(0.001
m) 2.21 x 109 F (Very Small!!)
Lesson difficult to get large values of
capacitance without special tricks!
8
Isolated Parallel Plate Capacitor
  • A parallel plate capacitor of capacitance C is
    charged using a battery.
  • Charge Q, potential difference V.
  • Battery is then disconnected.
  • If the plate separation is INCREASED, does
    Potential Difference V
  • (a) Increase?
  • (b) Remain the same?
  • (c) Decrease?
  • Q is fixed!
  • C decreases (e0A/d)
  • QCV V increases.

9
Parallel Plate Capacitor Battery
  • A parallel plate capacitor of capacitance C is
    charged using a battery.
  • Charge Q, potential difference V.
  • Plate separation is INCREASED while battery
    remains connected.

Does the Electric Field Inside (a) Increase? (b)
Remain the Same? (c) Decrease?
  • V is fixed by battery!
  • C decreases (e0A/d)
  • QCV Q decreases
  • E Q/ e0A decreases

10
Spherical Capacitor
What is the electric field inside the capacitor?
(Gauss Law)
Radius of outer plate b Radius of inner plate
a
Concentric spherical shells Charge Q on inner
shell, Q on outer shell
Relate E to potential difference between the
plates
11
Spherical Capacitor
What is the capacitance? C Q/V
Radius of outer plate b Radius of inner plate
a
Concentric spherical shells Charge Q on inner
shell, Q on outer shell
Isolated sphere let b gtgt a,
12
Cylindrical Capacitor
What is the electric field in between the plates?
Gauss Law!
Radius of outer plate b Radius of inner plate
a
Length of capacitor L Q on inner rod, Q on
outer shell
Relate E to potential difference between the
plates
cylindrical Gaussian surface of radius r
13
Summary
  • Any two charged conductors form a capacitor.
  • Capacitance C Q/V
  • Simple CapacitorsParallel plates C e0
    A/d Spherical C 4p e0 ab/(b-a)Cylindrical
    C 2p e0 L/ln(b/a)

14
Capacitors in Parallel
  • A wire is an equipotential surface!
  • Capacitors in parallel have SAME potential
    difference but NOT ALWAYS same charge!
  • VAB VCD V
  • Qtotal Q1 Q2
  • CeqV C1V C2V
  • Ceq C1 C2
  • Equivalent parallel capacitance sum of
    capacitances

15
Capacitors in Series
  • Q1 Q2 Q (WHY??)
  • VAC VAB VBC
  • SERIES
  • Q is same for all capacitors
  • Total potential difference sum of V
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