CurrentCurrent• Electric Current (I)

– T he rate at which charge flows through a perpe ndicular surface

dQI

dt

C/s or Ampere, A

T he current has the same direction as the flow of positive charge.

CurrentCurrent• Direct Current (DC)

– The constant current in magnitude and direction

• Alternating Current (AC)– The current changing in magnitude and

direction all the time

CurrentCurrent

( )dQ nAv t q

( )dav d

nAv t qQI nqv A

t t

vd : drift speed of charge q

n : number of mobile charge carriers per unit volume

Quiz #1Quiz #1

• Consider positive and negative charges movin g horizontally through the four regions shown i n the figure . Rank the current in these four reg

ions, from lowest to highest.

current density current density• The current density (J)

– the current per unit area

d

IJ nqv

A

dJ nqv

current density current density• A current density J and an electric field E are establi

shed in a conductor whenever a potential differenc e is maintained across the conductor

J E

Ohm’s law

: conductivity

ResistanceResistance

b a

J I lV V V El l l I IR

A A

= 1/ : Resi st i vi ty

lR

A Resi st ance (.m)

RResistivityesistivity

ResistResistorsors

ResistanceResistance

ResistanceResistance and Temperature

0 01 ( )T T

0 T

0 01 ( )R R T T

temperature coefficient of resistivity

Conductor

Resistance and Temperature Resistance and Temperature

Semiconductor

superconductorsuperconductor

• a class of metals and com pounds whose resistance

decreases to zero when th ey are below a certain tem

perature Tc , known as the critical temperature

superconductorsuperconductor

• A small permanent magnet levitated a

bove a disk of the s uperconductor Ba

2Cu3O7 , which is at77 K.

Electrical Power Electrical Power ((PP))

• T he rate at which energy is delivered to a r esi st or

22( )V

P I V I RR

Example #7Example #7

• For t he t wo l i ght bul b s shown in f igure, rank t

he cur r ent val ues at p oi nt s a t hr ough f , from

gr eat est t o l east

Direct Current Circuits Direct Current Circuits

• Electromotive Force• Resistors in Series and Parallel• Kirchhoff’s Rules• RC Circuits• Electrical Meters

Electromotive Force Electromotive Force

• Describing not a force but rather a potential difference in volts

• A battery is called either a source of electromotive force, or more commonly, a source of emf

Electromotive Force Electromotive Force

• The emf of a battery is the maximum possible voltage that the battery can provide between its terminals

Circuit Diagram

2 2Power I I R I r

a bV V V Ir

IR Ir IR r

r = internal resistance

R = load resistance

Example #8Example #8

• A battery has an emf of 12.0 V and an internal resistance of 0.05 . Its terminals are connected to a load resistance of 3.00 .

Resistors in Series

1 2 1 2( ) eqV IR IR I R R IR 1 2eqR R R

Resistors in Parallel

1 21 2 eq

V V VI I I

R R R

1 2

1 1 1

eqR R R

Example #9Example #9

• Four resistors are connected as shown in the figure, – Find the equivalent

resistance between points a and c

– What is the current in each resistor if a potential difference

of 42 V is maintained between a and c

Example #10Example #10

• Three resistors are connected in parallel as shown in the figure 28.11 . A potential difference of 18.0 V is maintained between points a and b– Find the current in each resistor– Calculate the power delivered to

each resistor and the total power delivered to the combination of resistors

– Calculate the equivalent resistance of the circuit

Kirchhoff’s Rules• Junction rule.

– The sum of the currents entering any junction in a circuit must equal the sum of the currents leaving that junction

in outI I

Kirchhoff’s Rules• Loop rule.

– The sum of the potential differences across all elements around any closed circuit loop must be zero

0CosedLoop

V

Example #11Example #11

• A single-loop circuit contains two resistors and two batteries, as shown in the figure (Neglect the internal resistances of the batteries.– Find the current in the circuit.– What power is delivered to each

resistor? – What power is delivered by the 12-V

battery?

Solution #11Solution #11

The 12-V battery delivers power

Example #12Example #12

• Find the currents I1, I2, and I3 in the circuit shown in the figure.

Solution #12Solution #12

RC Circuits• Charging a Capacitor

0q

IRC

RC Circuits• Charging a Capacitor

0

t

RCI I e

Q C

0IR

current at t = 0

maximum charge

( ) 1t

RCq t Q e

time constant of the circuit

RC

RC Circuits• Discharging a Capacitor

( 0)q t Q 0q

IRC

Charge at t = 0

( )t

RCq t Qe

0

( )( )

t t

RC RCdq t QI t e I e

dt RC

Electrical Meters• The Galvanometer

– the main component in analog meters for measuring current and voltage

Electrical Meters• The Ammeter

– A device that measures current

Electrical Meters• The Voltmeter

– A device that measures potential difference

Quiz #2Quiz #2• Find the equivalent resis

tance between points a and b i n the fi gur e

• If a pot ent i al di ff er en ce of 34.0 V i s appl i ed

between points a and b. c alculate the current in e

ach resistor.