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. 9/10/2018

A d Capacitance Parallel Plates Cylindrical Capacitor 9/10/2018

Question A +Q charge is placed on a solid spherical conductor. A -Q charge is placed on a concentric conducting spherical shell. Let V1 be the potential difference between the spheres with (a1, b). Let V2 be the potential difference between the spheres with (a2, b). What is the relationship between V1 and V2? a2 b +Q -Q a1 V2 < V1 (a) V1 < V2 (c) V1 > V2 (b) V1 = V2 9/10/2018

Comments on Circuit Diagrams: 1 2 a b 3 Wires have no electrical resistance. Components are ideal PHYS241 only deals with: Resistors, R Capacitors, C Inductors, L Batteries, Generators, switches & wires 9/10/2018

Equivalent Capacitors b Q2 Q1 C3 Q3 V C a b Q a b +Q -Q V -Q C a b +Q 9/10/2018

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. V C1 C2 a b Q2 Q1 C3 Q3 9/10/2018

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 b +Q -Q V 9/10/2018

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 b +Q -Q V 9/10/2018

Example C1 C2 C3 a b C a b 9/10/2018

Question What is the equivalent capacitance, Ceq, of the combination? (a) Ceq = (3/2)C (b) Ceq = (2/3)C (c) Ceq = 3C 9/10/2018

Question What is the relationship between V0 and V ? V0 V conductor (Area A) +Q (Area A) d/3 V0 V d conductor d/3 -Q -Q (a) V = (2/3)V0 (b) V = V0 (c) V = (3/2)V0 9/10/2018

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. 9/10/2018

Demo: Dielectrics & Capacitance –––––– ++++ ++++ ––––– + + E0 k 9/10/2018

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. 9/10/2018

Dielectric Properties material k dielectric strength (kV/mm) air (1 atm) 1.00054 3 paraffin 2.1–2.5 10 glass (Pyrex) 5.6 14 mica 5.4 10–100 polystyrene 2.55 24 H2O (200 C) 80 ? titania ceramic 130 strontium titanate 310 8 9/10/2018

Effect of Dielectrics on the Electric Field real charge real charge + - 9/10/2018

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 9/10/2018

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. 9/10/2018

Dielectric Combinations k1 d/2 A k2 d/2 A/2 A/2 d k2 d k1 9/10/2018

(1) (2) (3) (A) 1 (B) 2 (C) 3 (D) None 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) 3C S C 6q 3q 2C S C 6q 3q Left-hand increase (2) Left hand decrease (3) Remains the same (1) Both capacitors must have the same potential difference. (3) 2C S 2 C 6q 3q (A) 1 (B) 2 (C) 3 (D) None 9/10/2018

Summary Capacitors in parallel and in series Electric response of dielectric materials atomistic view polarized atoms dielectric constant 9/10/2018