Last Time Equilibrium vs. Steady State in a Circuit What is "used up" in a circuit? Kirchhoff's Current Node Law E-field inside a wire 1

Electric Field Inside the Wire Constant current in the wire  Constant E in the wire. I I I I I I I I Conventional Current Drift Velocity controlled by |E| Mobility (u) set by the material. Constant current requires constant |E| 2

Today Transient response when connecting a circuit How long until steady state is reached? Introduction to Resistors Energy conservation in a circuit Kirchhoff's Voltage Loop Law Batteries 3

Does current fill the wire? Is E uniform across the wire? E must be parallel to the wire E is the same along the wire 00V AB V CD Direction of Electric Field in a Wire 4

E Bulb filament and wires are metals – there cannot be excess charges in the interior Are excess charges on the battery? ASSUME: E due to dipole field of battery. E E What charges make the electric field in the wires? Electric Field in a Wire This cannot be the source of the E which drives current. 5

Surface charge arranges itself in such a way as to produce a pattern of electric field that follows the direction of the wire and has such a magnitude that current is the same along the wire. Field due to the Battery 6

Smooth transition from + surface charge to – to provide constant E. E Field due to Battery The amount of surface charge is proportional to the voltage. 7

Connecting a Circuit What happens just before and just after a circuit is connected? Before the circuit is connected: No current flows System is in equilibrium: There must be surface charges on the wire to prevent current from flowing before we connect the circuit. 8

Connecting a Circuit Before the circuit is connected: No current flows System is in equilibrium: Think about the gap... E due only to gap faces What happens just before and just after a circuit is connected? 9

Connecting a Circuit Before the circuit is connected: No current flows System is in equilibrium: Think about the gap... E due to everything else cancels E gap What happens just before and just after a circuit is connected? 10

Connecting a Circuit Now close the gap... E due to everything else cancels E gap What happens just before and just after a circuit is connected? Before the circuit is connected: The gap face charge  0, and so does E gap No more charges here 11

Connecting a Circuit What happens just before and just after a circuit is connected? Just after the circuit is connected: There is a disturbance in the previous (equilibrium) E-field. Now the region next to the disturbance updates its E-field, and the next region... How fast does this disturbance propagate? At the drift speed of the electrons? At the speed of light? 12

iClicker – Reality Physics! Drift speed of electrons Speed of light Flip Light Switch On. How long until electrons from the switch reach the light bulb? L = 5 m A) About 1 nanosecond B) About 1 microsecond C) About 1 minute D) About 1 day 13

iClicker – Reality Physics! Drift speed of electrons Speed of light Flip Light Switch On. How long until information about the change in E-field reaches the light bulb? L = 5 m A) About 16 nanoseconds B) About 16 microseconds C) About 16 minutes D) About 16 days 14

Reality Physics! Drift speed of electrons Speed of light Flip Light Switch On. How long until information about the change in E-field reaches the light bulb? L = 5 m ≈ 1 day for electrons to travel from light switch to bulb. ≈ 16 nanoseconds for the change in E-field to travel from light switch to bulb. Because there are sooooo many electrons in the wire, they don't have to move far to create a large current. 15

Connecting a Circuit What happens just before and just after a circuit is connected? Just after the circuit is connected: There is a disturbance in the previous (equilibrium) E-field. Now the region next to the disturbance updates its E-field, and the next region... The disturbance travels at the speed of light, and within a few nanoseconds, steady state is established. 16

After steady state is reached: Electric field in Thin and Thick wires 17

A Wide Resistor low mobility 18

Energy conservation (the Kirchhoff loop rule [2 nd law]):  V 1 +  V 2 +  V 3 + … = 0 along any closed path in a circuit  V wire = EL  V battery = ?  V=  U/q  energy per unit charge Energy in a Circuit 19

 V 1 +  V 2 +  V 3 +  V 4 = 0 (V B -V A )+ (V C -V B )+ (V F -V C )+ (V A -V F )=0 General Use of the Loop Rule 20

Why light bulb is brighter with two batteries? Work per second: Two Batteries in Series Two batteries in series can drive more current: Potential difference across two batteries in series is 2emf  doubles electric field everywhere in the circuit  doubles drift speed  doubles current. 21

non-Coulomb force on each e 1. a=F NC /m ECEC FCFC 2. F C =eE C Coulomb force on each e 3. F C =F NC The function of a battery is to produce and maintain a charge separation. Energy input per unit charge emf – electromotive force The emf is measured in Volts, but it is not a potential difference! The emf is the energy input per unit charge. chemical, nuclear, gravitational… Potential Difference Across the Battery 22

Nichrome wire (resistive) iClicker Questions When wire length double, the current will be A.Double B.Halved C.unchanged 23

Nichrome wire (resistive) Twice the Length Quantitative measurement of current with a compass Current is halved when increasing the length of the wire by a factor of 2. 24

iClicker Question Nichrome wire (resistive) When wire cross sectional area is doubled, the current will be A.Double B.Halved C.unchanged 25

Doubling the Cross-Sectional Area Nichrome wire If A doubles, the current doubles. 26

iClicker Questions When plug in two batteries instead of one, the current will be A.Double B.Halved C.unchanged 27

Why light bulb is brighter with two batteries? Work per second: Two Batteries in Series Two batteries in series can drive more current: Potential difference across two batteries in series is 2emf  doubles electric field everywhere in the circuit  doubles drift speed  doubles current. 28

How Do the Currents Know How to Divide? 29

Let’s be Quantitative Capacitors, Resistors and Batteries 30

Capacitor: Charging and Discharging ChargingDischarging 31

Similar to a large parallel plate capacitor s D Capacitor: Construction and Symbols There is no connecting path through a capacitor 32

Capacitor: Discharge Electron Current Electric Field 33

Capacitor: Charging 34

Capacitor: Charging Ultimately, the fringe field of the capacitor and the field due to charges on the wire are such that E=0 inside the wire. At this point, i=0. Why does current ultimately stop flowing in the circuit? 35

Thick filamentThin filament Which light bulb will glow longer? Why? 1)Round is brighter  capacitor gets charged more? 2)Long bulb glows longer  capacitor gets charged more? The Effect of Different Light Bulbs After current stops, Voltage across capacitor = Voltage across battery no matter which bulb is used. Capacitor charged by same amount in both cases. 36

Use two different capacitors in the same circuit In the first moment, which capacitor will cause the bulb to produce more light? Which capacitor will make the light bulb glow longer? Fringe field: Effect of the Capacitor Disk Size 37

In the first moment, which capacitor will cause the bulb to produce more light? Fringe field: Which capacitor will make the light bulb glow longer? Effect of the Capacitor Disk Separation 38

In the first moment, which capacitor will cause the bulb to produce more light? Fringe field: Which capacitor will make the light bulb glow longer? Insulator Effect of Insulator in Capacitor 39

The capacitors shown are initially uncharged. When connected to identical circuits, after 0.01 s of charging: A)The fringe field of each capacitor is the same. B)The fringe field of the smaller capacitor is greater. C)The fringe field of the larger capacitor is greater. R1R1 s s R2R2 40

Initial moment: brighter? Will it glow longer? Parallel Capacitors Fringe field: Capacitors in parallel effectively increase A 41

Will it glow at all? How do electrons flow through the bulb? An Isolated Light Bulb 42

Charging time I Bulb Brightness time E cap Energy conservation Capacitor in a Circuit Do 19.X.7! 43

I 1 = I 2 + I 3 Charge conservation: I i > 0 for incoming I i < 0 for outgoing Capacitor transients: not a steady state! Cannot use Kirchhoff rule for a part of a capacitor (area 1 or 2) But can use for capacitor as a whole (area 3) The Current Node Rule in a Capacitor Circuit …in steady state 44

Electric field in a capacitor: E s +Q -Q In general: Definition of capacitance: Capacitance Capacitance of a parallel- plate capacitor: Capacitance 45

A capacitor is formed by two rectangular plates 50 cm by 30 cm, and the gap between the plates is 0.25 mm. What is its capacitance? Exercise 46

s D No insulator:With insulator: A Capacitor With an Insulator Between the Plates 47