Phys. 122: Tuesday, 20 Oct. HW 8: due by 2:00 pm. Written HW 9: ch. 30, probs. 28, 40, and ch. 31, probs. 6,20, 42, and 46. Due a week from Thursday (29 Oct.). Mast. Phys.: assign. 6 due in one week. Reading: Finish ch. 31 by Thursday. Exam 1 curve: All scores were boosted up by 0.5 point (on topof test correction and/or bonus problem points); this is NOT shownon your exam but it is in the gradebook. Exam 2: will cover chapters 25 through 28; after HW 7 hasbeen returned (very likely Tuesday the 27th). Study guide and sampleexam problems have been updated and are available. Midterm Grades: I will post detailed grade breakdowns onCanvas later this week; please be patient!

Clickers: to find the total energy storedin a capacitor,

a) Use Q times V b) Use E² times ε₀, integrated over volume c) Add half of (a) to half of (b) d) Add all of (a) to all of (b) e) Use either half of (a) or half of (b), but not both

Energy storage in capacitors:Half what you might guess!

UC = Q V/2 Combine with Q = C V and we get two other, equivalent forms. (These other forms are good for

expressing the energy in terms of either the charge or the voltage.)

Another way to do the energy“book-keeping” in capacitors:

(The reason for giving you this extra way of finding theenergy is that it's ALWAYS TRUE, even for other electricfields besides capacitors! In fact, it's part of the energyof electromagnetic waves, including visible light.)

• Don't add this energy to the chargeor voltage capacitor energy! It's theexact same thing.

Dielectric: An insulator which is placedin between the conductors of a capacitor (gives C = κ C0)

Two important numbers for a dielectric: thedielectric constant (κ) and the maximum Efield strength before it sparks (breakdown E)

Dielectrics are a great way to boost C (to κ C₀),but they also lower the maximum E the capacitorcan handle before sparking (which can ruin the capacitor!)

Current is the net motion of charge (positivecharge moving along I, negative charge movingagainst I, or both).

Water Analogy: Electrical current is just like currentof a stream, river, or pipe. Both are measured in amountof stuff per time (that you would catch in a bucket).

Clickers: It's a constant trouble to keep track of the minus sign in the electron's

charge! Whom should you blame??

• a) Thomas Edison• b) Knight (your textbook author)• c) Thomas Jefferson• d) Benjamin Franklin• e) Nikola Tesla

Clickers: We've said that a conductor issomething which has lots of charges that

can flow freely. What is a superconductor?

• a) A metallic hero who keeps ordinary conductors safe from criminals

• b) A conductor whose charges are all free to move c) A conductor that can conduct current across

both space and time

• d) A conductor held at dangerously high voltage

• e) Just what we've been calling a conductor so far

Actual motion in an imperfect conductor isvery irregular; only the average motion(called the drift velocity) contributes to I.

(conductivity) σ = 1/ρ (resistivity)

At first glance, Ohm's Law should bother you!

Clickers: the units of current densityJ are...

a) Amps b) Coulombs per cubic meter c) Amps per cubic meter d) Amps per square meter e) Amps per meter

(conductivity) σ = 1/ρ (resistivity)

Let's figure out the macroscopic (total) version:

Some circuit diagram elements

Rule: treat wires as perfect conductors incircuit diagrams. (Actual resistive wirescan have their R put in series with the wireon the diagram.)

Clickers: What is the current through the3 Ω resistor?

a) 3 Ampsb) 2 Ampsc) 1 Ampd) 9/8 Ampe) 0 Amps

The fluid (water) analogy... updated

Electrical Thing Charge Voltage Electric Field Superconductor Capacitor Current (in a wire) Resistor Resistivity

Fluid thing Fluid (water) Pressure Pressure difference (Unrestricted) pipe Water tank Current (in a pipe) Pipe filled with sand Density of sand

A very simple series network

Parallel and Series Resistors

In Parallel, the voltage drop across any item is always the same as each of the others. Check for uninterrupted conductors connecting each side to

identify things in parallel in a circuit diagram.Parallel: 1/Req. = 1/R1 + 1/R2 + ...

(Currents in parallel add to give the total current.)

In Series, the current through each item is the same.(For capacitors, this meant the charges were equalafter the capacitors became charged.) Look for asingle wire broken only by the items, to identify aseries network.

Series: Req. = R1 + R2 + ...(Voltage drops in series add to give the total.)

Clickers: why are the series andparallel rules backward for resistors

versus for capacitors? a) Because capacitors are like inverse resistors: larger C means smaller R

b) Because capacitors are like negative resistors

c) Because the voltage rules for R and C are flipped

d) To confuse physics students e) To confuse physics professors

This is the formula for the power acrossanything in a circuit. It might stand forpower being lost, being stored, or beingused in some useful way.

Clickers: For a resistor in a circuit,what does the power represent in

P = I ΔV ?

• a) Energy per time being used by the resistor b) Energy per time being stored in the resistor

• c) It depends upon the relative direction of I and the difference in potential

• d) The power being stored by capacitors in the same circuit

• e) The power gained by each electron

Clickers: For a capacitor in a circuit,what does the power represent in

P = I ΔV ?

• a) Energy per time being stored in the capacitor

• b) Energy per time being released from it

• c) It depends upon the relative direction of I and the difference in potential

• d) The power is being used by resistors in the same circuit

• e) The power gained by each electron