Chapter 17: Current and Resistance Electric Current Definition of electric current A current is any motion of charge from one region to another. Suppose.

Chapter 17: Current and ResistanceElectric Current

Definition of electric current

A current is any motion of charge from one region to another.

• Suppose a group of charges move perpendicular to surface of area A.

• The current is the rate that charge flows through this area:

t

Qt

QI

interval time theduring

flows that charge ofamount ; SI unit: 1 A = 1 ampere = 1 C/s

Homework assignment : 18, 38, 51, 60, 67

Example 17.1 : Turn on the light

Electric Current

• The amount of charge that passes through the filament of a certain lightbulb in 2.00 s is 1.67 C. Find(a) the current in the bulb and (b) the number of electrons that passthrough the filament.

(a) A 835.0s 2.00

C 67.1

t

QI

(b) electrons 1061.2sC/electron 1061.2

s) A)(5.00835.0( 1919

q

tINtINq

Microscopic view of current

A Microscopic View of Current

Microscopic view of current (cont’d)

A Microscopic View of Current

Microscopic view of current (cont’d)

• In time t the electrons move a distance tx d • There are n particles per unit volume that carry charge q

• The amount of charge that passes the area A in time t is

)( tnAqQ d • The current I is defined by:

Anqt

QI d

A Microscopic View of Current

Example 17.2 : Drift speed of electrons

A copper wire of cross-sectional area 3.00x10-6 m2 caries a currentof 10.0 A.(a) Assuming that each copper atom contributes one free electron to the metal, find the drift speed of the electrons in this wire.

33

cm 12.7g/cm 8.92

g 5.63

m

V

A Microscopic View of Current

vol. of one mole of copper

363 m 1012.7cm 12.7

32836

23

melectrons/ 1046.8mole/m 1012.7

moleelectrons/ 1002.6

n

m/s 1046.2)m 10C)(3.00 1060.1)(e/m 10(8.46

C/s 0.10 42619328

nqA

Ivd

(b) Using the ideal gas model to compare the drift speed with the random rms speed an electron would have at 20.0oC.

m/s 1015.1kg 1011.9

K) J/K)(293 1038.1(33 531

23

e

Brms m

Tkv

Circuit diagram

Current and Voltage Measurements in Circuits

A

V

+

+

-

-Voltmeter

Ammeter

Bulb

+-

BatteryAmmeter : measures the currentVoltmeter: measures the electric potential difference

Resistance and Ohm’s law

Resistance and Ohm’s Law

• When a voltage (potential difference) V is applied across the ends of a metallic conductor, the current in the conductor is found to be proportional to the applied voltage:

E

I

Vb

Va

A

V=Vb-Va

IRRIV The proportionality constantis called resistance. SI unit isohm (

I

VR

Ohm’s law

• A resistor is a conductor that provides a special resistance in an electrical circuit: Symbol

SI unit: ohm () = volt/amper (V/A)

Resistance and Ohm’s law (cont’d)

Resistance and Ohm’s Law

• For many materials, including most metals, the resistance remains constant over a wide range of applied voltages or currents.

• Materials that obey the Ohm’s law over a wide range of voltage are said to be ohmic. Otherwise they are said to be nonohmic.

V

V

resistor that obeysOhm’s law

semiconductordiode

Resistivity

Resistivity

• The resistance of an ohmic conductor increases with length . The electrons go through the conductor encounter more collisions

• A smaller cross-sectional area A also increases the resistance of a conductor.

A

lR

: resistivity : lengthA : area

Resistivity and temperature• The resistivity of a metallic conductor nearly always increases with increasing temperature.

)](1[)( 00 TTT reference temp. (often 0 oC)

temperature coefficient of resistivity

Material oC)-1

aluminum

brass

graphitecopper

0039.0

0020.00005.000393.0

iron

leadmanganin

silver

0050.0

00000.0

0038.0

0043.0

Material oC)-1

Temperature Variation of Resistance

)](1[)( 00 TTRTR

platinum 00392.0

Example 17.5 : A platinum resistance thermometer• A resistance thermometer, which measures temperature by measuring the change in resistance of a conductor, is made of platinum and has a resistance of 50.0 at 20.0oC. (a) When the device is immersed in a vessel containing melting indium, its resistance increases to 76.8 . From this information find the melting point of indium.

Temperature Variation of Resistance

C157C137) 0.50](C)(1092.3[

50.0- 8.761-3

0

00

TR

RRTT

(b) The indium is heated further until it reaches a temperature of 235oC. What is the ratio of the new current in the platinum to the current Imp at the melting point?

)](1[

)](1[

mpmp

mpmp

TTI

V

I

V

TTRR

766.0

)(1

1

mpmp TTI

I

Superconductors Resistivity vs. temperature and superconductor

• The resistivity of graphite decreases with the temperature, since at higher temperature more electrons become loose out of the atoms and more mobile.

• This behavior of graphite above is also true for semiconductors.

• Some materials, including several metallic alloys and oxides, has a property called superconductivity. Superconductivity is a phenomenon where the resistivity at first decreases smoothly as the temperature decreases, and then at a certain critical temperature Tc the resistivity suddenly drops to zero.

T

T

TTc

metal semiconductor superconductor

Electrical energy and power• A battery is used to establish an electric current in a conductor by converting chemical energy stored in the battery into kinetic energy of the charged carriers such as electrons.

Electrical Energy and Power

• The kinetic energy of the carriers is lost as a result of collisions between the charge carriers and fixed atoms in the conductor (resistance).

ground

A

B C

D

Point A : reference point VA=0 (grounded)• Imagine the charge moves from A to B to

C to D to A.A-B : Energy increases by VQB-C : No change in energy

C-D : Energy decreases by VQ

PVIVt

Q

Energy

lost int

Powerlost toresistor

RIIRIVIP 2)( SI unit : watt (W)

Example 17.7 : The power converted by an electric heater• An electric heater is operated by applying a potential difference of 50.0 V to a nichrome wire of total resistance 8.00 . (a) Find the current carried by the wire and the power rating of the heater.

Electrical Energy and Power

A 25.6 8.00

V 0.50

R

VI

W00.8()A 25.6( 22 RIP

(b) Using this heater, how long would it take to heat 2.50x103 moles of diatomic gas (e.g. a mixture of oxygen and nitrogen-air) from 10.0oC to 25.0oC? Take the molar specific heat at constant volume of air to be (5/2)R.

J 107.79K) 283K K)](298J/(mol 31.82

5mol)[ 1050.2( 53 TnCUQ V

U=Q+W and W=0

s 1049.2 W313

J1079.7 35

P

Qt

Heart and electrocardiograph• Every action involving the body’s muscles is initiated by electrical activity.

Electrical Activity in the Heart

• The voltage produced by muscular action in the heart are particularly important to physicians. Voltage pulses cause heart to beat, and the waves of electrical excitation that sweep across the heart associated with the heartbeat are conducted through the body via the body fluids.

• These voltage pulses can be detected by an equipment attached to the skin.

• This equipment electro- cardiograph is basically made of a voltmeter that measures pulses in 1 mV range.

Sinoartrial (SA) node

RA

LA

RL

LV

RA: right atrium, LA: left atrium, RV: right ventricle, LV: left ventricle

Atrioventricular (AV) node

• The pattern recorded by this device is called electro- cardiogram.

Heart activity and EKG• As the SA node fires, each electrical impulse travels through the right and left atrium.

Electrical Activity in the Heart

• This electrical activity causes the two upper chambers to contract. This activity is recorded as “P-wave” on EKG.• The electrical impulse then moves to an known as the AV node just above the ventricles. Here the electrical impulse is held up for a brief period. This delay allows the right and left atrium to empty the blood into the two ventricles. This delay is recorded as “PR interval” on EKG.

• After the delay, the impulse travels through both ventricles and cause them to contract, and the blood is emptied into the pulmonary artery and aorta. This activity is recorded as “QRS-complex” on EKG.• Then ventricles recover from its electrical stimulation and generate an “ST-segment” and T waves on EKG.