Capacitors Q D A capacitor is a device that is capable of storing electric charges and thus electric potential energy. => charging Its purpose is to release them later in a controlled way. => discharging Capacitors are used in vast majority of electrical and electronic devices. +Q -Q Typically made of two conductors and, when charged, each holds equal and opposite charges.

DOCCAM 2 DEMO 5A-28 PARALLEL PLATE CAPACITOR

Polar and Nonpolar Dielectrics Polar dielectrics: dielectric material whose molecules have permanent electric dipole moments, such as water. Eext = 0: the orientations of the permanent electric dipoles are distributed randomly, so the net dipole moment of the material is zero. Eext > 0 : the molecular dipoles try to align themselves with the field against random thermal motion, resulting in a net dipole moment. Nonpolar dielectrics: molecules with no permanent electric dipole moments. Eext > 0 : ± charges separate, induced dipole moment emerges. Show the first demo:5A-31

READING QUIZ 1 A capacitor C0 with air dielectric κ =1 is charged to a potential V and then is disconnected from the battery. A uniform dielectric with dielectric constant κ > 1 is inserted into the capacitor and occupies the full volume of the capacitor. If the original electric field is E0 and the final electric field is Eκ , which of the following statements is correct.? A| E0 = Eκ B| E0 < Eκ C| E0 > Eκ D| E0 = Eκ / κ

Dielectrics between Capacitor Plates + Q - Q free charges Electric field E between plates can be calculated from Q – q. neutral -q +q Polarization Charges ± q The presence of a dielectric weakens the electric field, therefore weaken the potential drop between the plates, and leads to a large capacitance.

DOCCAM 2 DEMO 5A-30 EFFECT OF DIELECTRICS ON CAPACITANCE

Inserting Dielectrics (= Insulator) Inserting a dielectric between the plates of a capacitor increases capacitance Q=CV holds more charges at fixed V Dielectric constant κ of a dielectric is the ratio of the capacitance when filled with it to that without it: κ > 1 always (dimensionless) Material κ air (1 atm) 1.00059 paper 3.7 pyrex 5.6 water (20 o C) 80.4 strontium titanate 310 Under the same Q, V = V0/k E = E0/k Show demo: 5A-30 Breakdown potential determined by dielectric strength (Emax)

Capacitors in Parallel V is common Equivalent Capacitor: where

Capacitors in Series q is common Equivalent Capacitor: where

Conductor inserted between plates A parallel-plate capacitor with conductor inserted in the middle Two capacitors of area A in series +q +q a -q -q -Q -Q +q +q b -q -q E=0 outside capacitors E=0 in conductor between plates between plates (a)

Warm-up quiz 2 All the capacitors have the same capacitance C, What is the total capacitance between A and B? A B A). 4/3 C B). 3/4 C C). 3/2 C D). 1/2 C E). 2/3

Non-uniform Parallel-plate Capacitor 1 Equivalent to 2 capacitors in parallel Potential drop V in each is the same. Note a if even though

Non-uniform Parallel-plate Capacitor 2 Equivalent to 2 capacitors in series (Free) charge in each Q is the same. a Note if

Inserting Dielectric Material with Battery Disconnected Charge a parallel plate capacitor filled with air (or vacuum) to potential difference V0. Deposits charge Q 2. Disconnect the battery Q remains fixed -Q 3. Insert a dielectric of dielectric constant κ Q So, V and E decreases from V0 , E0 to and -Q and

Energy stored in a capacitor revisited +Q -Q Battery disconnected Separation ~ 0 +Q -Q Change in separation Δ d External work required to separate the plates from zero to d m apart is What if a battery remains connected?

Inserting Dielectric Material with Battery Connected Charge a parallel plate capacitor filled with vacuum (air) to potential difference V. Deposits charge 2. Keep the battery connected V remains fixed 3. Insert a dielectric of dielectric constant κ So, Q increases from Q0 and E remains fixed and and

Force and energy with battery connected, a mystery? Force between plates? +Q -Q Battery connected V attractive Work to change separation from 0 to d? Separation ~ 0 +Q -Q Q changes Separation Δ d Separation d+Δd Separation d However, Why? Battery must be included in energy conservation !

Lecture 10:30 quiz 3 September 20, 2011 Five identical capacitors have the same capacitance C. Then capacitor (e) is filled with a material with dielectric constant k. What is the capacitance from A to B? a b e A B c d A). 2C B). 1/(1+k) C C). (1+k)C D). 5 C E). [4/(4+k)] C

Lecture 11:30 quiz 3 September 22, 2011 Five identical capacitors have the same capacitance C. Then capacitor (e) is filled with a material with dielectric constant k. What is the total capacitance from A to B? a b e A B c d A). 2C B). [k/(1+k)] C C). (1+k)C D). [1/(1+k)] C C E). (4+k) C

Lecture 11:30 quiz 3, February 8, 2011 Four identical capacitors have the same capacitance C. Then capacitor (a) is filled with a material with dielectric constant k. What is the total capacitance from A to B? a b A B c d A). (3/2 + k) C B). (3+k) C C). 5/2 C D). (2/3 +k) C E). (3+k) C