adftdagenda for today - department of physicsameyerth/phy132s15/lect15_pl.pdf · adftdagenda for...

Physics 132: Physics 132: Lecture 15Lecture 15ys cs 3ys cs 3 ectu e 5ectu e 5Elements of Physics IIElements of Physics II

A d f T dA d f T dAgenda for TodayAgenda for Today ResistanceResistance ResistorsResistors SeriesSeries ParallelParallel

Ohm’s lawOhm’s lawElectric CircuitsElectric Circuits Electric CircuitsElectric Circuits CurrentCurrent Kirchhoff’s lawsKirchhoff’s laws

Physics 202: Lecture 5, Pg 1

Kirchhoff s lawsKirchhoff s laws

Electric CurrentElectric CurrentH d it t di h d? How does a capacitor get discharged?

Figure (a) shows a charged capacitor in equilibrium.Figure (b) shows a wire discharging the capacitor Figure (b) shows a wire discharging the capacitor.

As the capacitor is discharging, there is a current in the wire.


Th t l t f t lCharge Carriers

The outer electrons of metal atoms are only weakly bound to the nuclei.

In a metal, the outer electrons become detached from their parent nuclei tofrom their parent nuclei to form a fluid-like sea of electrons that can move through the solidthrough the solid.

Electrons are the charge carriers in metals.


A Model of Conduction

Within a conductor in electrostaticelectrostatic equilibrium, there is no electric field.

In this case, an electron bounces back and forth between collisions, but its average velocity is zerozero.


A Model of Conduction

• In the presence of an electric field, the

l t i felectric force causes electrons to move along parabolicalong parabolic trajectories between collisions.

• Because of the curvature of the t j t i th itrajectories, there is a slow net motion in the “downhill” direction.


downhill direction.

PlinkoPlinko Disks = electrons Disk bounces through atoms on it’s

way down the inclineway down the incline Angle of incline = emf (potential

difference) ) Youtube demo


Discharging a Capacitor

How long should it take to discharge this capacitor?capacitor?

A typical drift speed of electron current h h i ithrough a wire is

vd 104 m/s. At this rate it wouldAt this rate, it would

take an electron about 2000 s (over half an hour) to travel 20 cmhour) to travel 20 cm.


Discharging a Capacitor

The wire is already full The wire is already full of electrons!

We don’t have to wait for electrons to move all the way through the wire from one plate to another.

We just need to slightly rearrange the chargesrearrange the charges on the plates and in the wire.


Creating a CurrentCreating a Current

A book on a table will l d d tslow down and stop

unless you continue pushing.

Analogously, the sea of electrons will slow down and stop unless youand stop unless you continue pushing with an electric field.


Electromotive forceElectromotive force

Electromotive force (emf) is the maximum Electromotive force (emf) is the maximum potential difference a battery or power source can give a circuit. A b h f f 12 V A car battery has an emf of 12 V

Sometimes shown as a script (E)

Symbol for emf-

+


Electrical CurrentElectrical Current

When we connect the two terminals of an emf to When we connect the two terminals of an emf to a circuit ( a continuous conducting path), charge will move continuously through the circuit.

Since there is a potential difference electrons in circuit will feel a force

Electrons will flow in direction of positive terminal

emfpositive terminal

Battery “pushes” electrons


Electrical CurrentElectrical Current

This flow is called electric current This flow is called electric current Net amount of charge through a point in

the circuit per unit time.

Units Ampere = Coulomb/second

QtQ I


Electric CurrentElectric Current The direction of current flow – from the positive terminal to

the negative one – was decided before it was realized that electrons are negatively charged Therefore current flowselectrons are negatively charged. Therefore, current flows around a circuit in the direction a positive charge would move; electrons move the other way. However, this does not matter in most circuitsnot matter in most circuits.


Establishing the Electric Field in a WireEstablishing the Electric Field in a Wire The figure shows two

metal wires attached to th l t f h d

gg

the plates of a charged capacitor.

This is an electrostaticThis is an electrostatic situation.

What will happen if we connect the bottomconnect the bottom ends of the wires together?


Establishing the Electric Field in a WireEstablishing the Electric Field in a Wire

Within a very brief

Establishing the Electric Field in a Wire

Within a very brief interval of time (109 s) of connecting the wires the sea ofthe wires, the sea of electrons shifts slightly.

The surface charge is rearranged into a nonuniformdistribution, as shown in the figure


Establishing the Electric Field in a Wire The nonuniform distribution of surface

charges along a wire creates a net electric field inside the wire that points from the morefield inside the wire that points from the more positive end toward the more negative end of the wire.

This is the internal electric field that pushes the electron current through the wire.


Give it a try:Give it a try:Surface charge is distributed on a wire as shown. Electrons in the wire

A. Drift to the right.gB. Drift to the left.C. Move upward.pD. Move downward.E. On average, remain at rest.


ResistanceResistance Resistance: Traveling through a conductor, electrons

b i t thi hi h l th dbump into things which slows them down. : Resistivity: Density of bumps L: Length of conductor A

LρR L: Length of conductor A: Cross sectional area of conductor

A

Aρ

A All electrical devices will resist

the flow of electrical currentL


PlinkoPlinkoALρR A


Ohm’s lawOhm’s law

Rule for current flow in most conductors: Rule for current flow in most conductors: Higher resistance leads to lower current Higher potential difference leads to higher current

IRV Ohm’s law

• Hi h i t l t

IRV Ohm s law

VI• Higher resistance lower current

Units are Ohms () RI


Ohm’s lawOhm’s law

IRV Ohm’s law

VI R


ResistorResistor

A device that resists current A device that resists current

Used to control current flow in a circuitUsed o co o cu e o a c cu

Resistor in a circuit:

Generally in a circuit the resistance of the connecting wires are very small and we canconnecting wires are very small and we can neglect them.

Wires will resist current, but we will assume


they have zero resistance!!

Battery-Wire-Resistor-Wire Circuity

The figure shows a The figure shows a resistor connected to a battery with current-carrying wirescarrying wires.

Current must be conserved; hence the current I through the resistor is the same as the current in each wire.


Kirchhoff’s Junction Law

For a junction, the law of conservation of current requires that

where the symbol ymeans summation.

This basic conservation statement is called Kirchhoff’s junction law


law.

Give it a try:Give it a try:

The current in the fourth wire is

A. 16 A to the right.B. 4 A to the left.C. 2 A to the right.D. 2 A to the left.E. Not enough information to tell.


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