252022 1 252022 2 Chapter 24 Capacitance Capacitor

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Chapter 24 Capacitance • Capacitor is a device that stores electrostatic potential energy. • A capacitor consists of 2 spatially separated conductors which can be charged to +Q and -Q. • The capacitance is defined as the ratio of the charge on one conductor of the capacitor to the potential difference between the conductors. 2/5/2022 3

Capacitance Parallel Plates A d Cylindrical Capacitor 2/5/2022 4

Question • A +Q charge is placed on a solid spherical conductor. A -Q charge is placed on a concentric conducting spherical shell. – Let V 1 be the potential difference between the spheres with (a 1, b). – Let V 2 be the potential difference between the spheres with (a 2, b). – What is the relationship between V 1 and V 2? -Q -Q +Q a 1 +Q b (a) V 1 < V 2 2/5/2022 (b) V 1 = V 2 a 2 b (c) V 1 > V 2 5

Comments on Circuit Diagrams: a C 3 b C 1 C 2 1. Wires have no electrical resistance. 2. Components are ideal 3. PHYS 241 only deals with: (a) Resistors, R (b) Capacitors, C (c) Inductors, L (d) Batteries, Generators, switches & wires 2/5/2022 6

Equivalent Capacitors a V b Q 1 C 1 Q 2 Q 3 C 2 C 3 a V a +Q -Q b 2/5/2022 C b a V Q +Q C -Q b 7

Capacitors in Parallel Capacitors connected in parallel can be replaced with an equivalent capacitor that has the same total charge, Q and the same applied potential V. a Q 3 Q 1 Q 2 V C 3 C 1 C 2 b 2/5/2022 8

Capacitors in Series Capacitors are in series when a potential difference that is applied across their combination is the sum of the resulting potential differences across each capacitor. a +Q -Q V +Q -Q b 2/5/2022 9

Capacitors in Series Capacitors that are connected in series can be replaced with an equivalent capacitor that has the same charge Q and the same total potential difference V as the actual series capacitors. a +Q -Q V +Q -Q b 2/5/2022 10

Example a C 3 b 2/5/2022 C 1 C 2 a b C 11

Question • What is the equivalent capacitance, Ceq, of the combination? o Ceq C C C o (a) Ceq = (3/2)C 2/5/2022 (b) Ceq = (2/3)C (c) Ceq = 3 C 12

Question • What is the relationship between V 0 and V ? +Q (Area A) V 0 d -Q (a) V = (2/3)V 0 2/5/2022 +Q (Area A) d/3 V -Q (b) V = V 0 d/3 conductor (c) V = (3/2)V 0 13

Dielectrics • Empirical observation: Inserting a non-conducting material between the plates of a capacitor changes the VALUE of the capacitance. • Definition: The dielectric constant of a material is the ratio of the capacitance when filled with the dielectric to that without it. 2/5/2022 14

Demo: Dielectrics & Capacitance – – – ++ ++ ++ + E 0 2/5/2022 – – – k 15

Dielectric Strength *The maximum value of the electric field that a dielectric material can tolerate before breaking down. * It limits the voltage that can be applied to a capacitor. The maximum voltage is called the breakdown potential. 2/5/2022 16

Dielectric Properties material air (1 atm) paraffin glass (Pyrex) mica polystyrene H 2 O (200 C) titania ceramic strontium titanate 2/5/2022 k dielectric strength (k. V/mm) 1. 00054 2. 1– 2. 5 5. 6 5. 4 2. 55 80 130 310 3 10 14 10– 100 24 ? 8 17

Effect of Dielectrics on the Electric Field real charge + + + + 2/5/2022 -+ -+ -+ -+ -+ real charge -+ -+ -+ 18

Capacitors with a dielectric for Fixed Amount of Charge For Fixed Charge, the insertion of a dielectric: : decreases the Electric Potential decreases the Electric Field decreases the Electric Potential Energy The decrease in energy can be accounted for by the work done in moving the dielectric slab between the plates of the capacitor 2/5/2022 19

Capacitors with a dielectric connected to a battery (Constant Potential). For a constant applied potential, the insertion of a dielectric: : increases the amount of charge on the plates increases the Electric Field increases the Electric Potential Energy The increase in energy occurs because work is done to maintain the potential across the plates as the dielectric is inserted. 2/5/2022 20

Dielectric Combinations k 1 k 2 A/2 k 1 2/5/2022 A A d d/2 A/2 k 2 d 21

QUIZ 9: Three circuits, each consisting of a switch and two capacitors are initially charged as indicated. After the switches have been closed, in which circuit will the charge on the capacitors remain the same? (1) (2) S (A) 1 (B) 2 (C) 3 (D) None 2/5/2022 3 q C 6 q 3 C 3 q C 6 q 2 C S S (3) 6 q 2 C 3 q 2 C 22

Summary • Capacitors in parallel and in series • Electric response of dielectric materials – atomistic view polarized atoms – dielectric constant 2/5/2022 23