chapter 19 current of electricity

CAMBRIDGE A – LEVEL

PHYSICS

ELECTRICITY

CURRENT OF

ELECTRICITY

L E A R N I N G O U T C O M E SNUMBER LEARNING OUTCOME

i R e c a l l c e r t a i n p r o p e r t i e s o f c h a r g e d p a r t i c l e s .

ii U n d e r s t a n d w h a t c a u s e s f r e e m o v i n g c h a r g e s t o f l o w

p r o d u c i n g e l e c t r i c c u r r e n t .

iii W h a t i s p o t e n t i a l d i f f e r e n c e ?

iv U n d e r s t a n d t h e c o n c e p t o f r e s i s t a n c e a n d u n d e r s t a n d i t s

r e l a t i o n s h i p w i t h e l e c t r i c p o w e r d i s s i p a t e d

v S k e t c h t h e c u r r e n t v s . p o t e n t i a l d i f f e r e n c e c u r v e s f o r

c e r t a i n m a t e r i a l s

vi U n d e r s t a n d O h m ’s L a w

vii U n d e r s t a n d t h e m e a n i n g o f r e s i s t i v i t y a n d r e l a t e i t t o t h e

r e s i s t a n c e o f a m a t e r i a l

viii U n d e r s t a n d t h e c o n c e p t o f t h e e l e c t r o m o t i v e f o r c e a n d

l e a r n h o w i n t e r n a l r e s i s t a n c e a f f e c t s p o t e n t i a l d i f f e r e n c e

a c r o s s a d . c . s o u r c e

P R O P E R T I E S O F C H A R G E D

PA R T I C L E S

P R O P E R T I E S O F C H A R G E D

PA R T I C L E S• Molecules that have an acquired an• Molecules that have an acquired an

excess of electrons will be negativelycharged, while molecules that areelectron deficient are positivelycharged.• Charged particles, whether positive or

negative will experience a force in anelectric field.• Charge is the property of matter that

will cause it to experience an electricforce in an electric field.

ELECTRIC CURRENT• Electric current is the net movement

no current

• Electric current is the net movement of charges from one region to another.

• When the electric field across a conductor is zero, there is no current even though some electrons are free to move about in random directions.

ELECTRIC CURRENT• What happens when we apply a• What happens when we apply a

electric field across the ends of aconductor?

• There will be a resultantdisplacement causing the electronsto drift in the direction of theelectric force causing a current toflow.

ELECTRIC CURRENT• The blue path indicates the path

of a random moving electron

without an E – field acting across

the conductor.

• The pink path shows the path of

an electron under the influence of

an external E – field.

• Notice that this produces a net

displacement on the electron.

• This net displacement produces a

flow of charges through the

conductor.

• This results in an electric current.

Diagram 25.1, page 819, Sear’s and Zemansky’s University Physics, Young and Freedman,

13th edition, Pearson Education, San Francisco, 2012.

ELECTRIC CURRENT• In conductors, the free

moving charges areelectrons.

• However, current is the netflow of positive particles.

Diagram 25.2, page 820, Sear’s

and Zemansky’s University Physics,

Young and Freedman, 13th edition,

Pearson Education, San Francisco,

ELECTRIC CURRENT• Assume we a conductor of cross

sectional area, ��.

• The amount of current flowing is

defined as the net charge

flowing through the cross

sectional area, per second.

• If is the net charge flowing

through the surface area � in

time �, then the current, � �

�• Unit of electric current = A

(Ampere)

Diagram 25.3, page 820, Sear’s and Zemansky’s University Physics, Young and

Freedman, 13th edition, Pearson Education, San Francisco, 2012.

ELECTRIC CURRENT• From the previous slide we have • From the previous slide we have

• The unit for Coulomb (C) or .

• Definition: “1 Coulomb is defined as the amount of electric charge carried by an electric current of 1 Ampere in 1 second.”

E X A M P L E S

Oct/Nov 2008, Paper 1, Question 34.

E X A M P L E S

H O M E W O R K

1. May/June 2009, Paper 1, question 30.

2. Oct/Nov 2010, Paper 12, question 31.

3. May/Jun 2011, Paper 11, question 31.

P OT E N T I A L D I F F E R E N C E

• As learned in the previous chapter, the• As learned in the previous chapter, thedirection of electric force on a chargedparticle in an E – field is opposite to thedirection of increasing electric potentialenergy.• Hence, (conventional ) current flows in

the direction of decreasing electricalpotential energy.• When current flows, the charges lose

electric potential energy.

• Since the amount of charges that flow is• Since the amount of charges that flow isgreat, another quantity is used tomeasure the change in electric potentialenergy that occurs.• This quantity is known as potential

difference.• Definition: “Potential difference is the

amount of electric energy transformedinto other forms, like heat, per unit ofcharge. ”

• The unit for potential difference is the • The unit for potential difference is the Volt (V) (or J/C).

• Definition: “1 Volt is the potentialdifference between two points when 1Joule of energy is transferred by oneCoulomb passing from one point to theother.”

• When charges flow, they flow

from a point higher potential

to a point with lower

potential.

• This causes the charges to

transfer their energy into

forms (e.g. heat, light).

• This energy transferred is the

potential difference between

the two points.

E X A M P L E S

May/June 2008, Paper 1, Question 33.

H O M E W O R K

RESISTANCE• When electric current flows, there is a

� �

• When electric current flows, there is aresistance offered by the ions in theconductor.

• This is due to the collisions that occurbetween the moving charges and the ions inthe conductor.

• Definition: “The electric resistance, � isdefined as the ratio of potential differenceacross (in V) to the amount of current (in A)that flows through a specific conductor” or

� �

RESISTANCE• The unit of electrical resistance is

��

• The unit of electrical resistance isthe ohm (Ω).

• Definition: “1 ohm is defined as theresistance of a conductor that has apotential difference of 1 volt when 1Ampere of current flows through it.”or

1 Ω =��

��.

RESISTANCE• When electric current flows through• When electric current flows through

certain elements, there is a decrease inelectric potential energy in the charges.

• What happens to this energy?• As the charges flow, they collide with the

ions of the element and the electricpotential energy is transferred to theions as internal energy.

• The increased internal energy will causeheat to be dissipated from the element.

RESISTANCE• Let us say that we need to do work,

• Let us say that we need to do work, to move Coulombs of charge

across a potential difference of V.This work, or

• Hence, we obtain ��

��.

• Electric power dissipated (in Watts), or � (since )

E X A M P L E S

H O M E W O R K

I – V C H A R AC T E R I S T I C S

and a filament lamp.

• We plot current (I) versus potential

difference (V) graphs to show how a

varying potential difference across a

specific material will affect the current

through the conductor.

• We will limit our discussion to a

constantan wire, a semiconductor diode

and a filament lamp.

Diagram 25.10 (a), page 827, Sear’s and Zemansky’s University Physics, Young and

The constantan wire

• The diagram shows the I – V

curve for a specimen of

constantan wire at a

constant temperature.

• The curve is a straight line

indicating a linear

relationship between

current, I and potential

difference, V.

Diagram 25.10 (a), page 827, Sear’s and Zemansky’s University Physics, Young and

• The slope of the straight line

passing through the origin

gives the inverse of the

resistance of the specimen, or�

�in Ω-1.

• When potential difference is

negative, current is also

negative indicating that when

the polarities of the ends are

reversed, the current will flow

in the opposite direction.

The semiconductor diode

• The diagram shows the I – V curve

for a specimen of a

semiconducting diode.

• For positive voltages, the current

increases non – linearly with the

potential difference across it once

the threshold voltage is crossed..

• For negative potential differences,

there will be a very small current

flowing, in the direction opposite

to the direction of the positive

current, up till before the

breakdown voltage.

Source: http://www.societyofrobots.com/images/DiodeChart.gif

• Diodes are devices that allow

current to flow in one

direction; i.e., a one – way

valve.

• To find the resistance of the

diode for a particular

voltage, V, we read off the

graph the value of current, I.

We then find the resistance,

R, as � �

Source: http://www.societyofrobots.com/images/DiodeChart.gif

The filament lamp

• The diagram shows the I – V

curve for a specimen of a

filament lamp.

• Initially, the current flowing in it

and the voltage across it are

linearly proportional.

• As the voltage increases, the

slope of the curve decrease.

This means that as the voltage

gets larger, the incremental rise

in current gets smaller.

Source: http://www.bbc.co.uk/schools/gcsebitesize/science/images/ph_elect14.gif

• This only could happen if the

resistance gets larger.

• Why does the resistance of the

filament lamp increase as voltage

across it gets larger?

• As the voltage across it gets larger,

the heat generated will be greater,

causing the metal ions to vibrate

with a greater amplitude. The

frequency of collisions between

charges and the metal ions will

increase. This leads to higher

resistance offered to current flow

by the filament.

Source: http://www.bbc.co.uk/schools/gcsebitesize/science/images/ph_elect14.gif

OHM’S LAW

• Definition: “Ohm’s Law states that for a

conductor at a constant temperature,

the current through it is directly

proportional to the potential difference

across it.”

OHM’S LAW• If we examine the I – V curves for the three devices

as shown above, only of the devices exhibits a

proportional relationship between current and

potential difference.

• This means that if we plot an I – V curve for a

material at a constant temperature and obtain a

linear relationship, that material obeys Ohm’s Law.

• For such devices, we can obtain the resistance by

finding the inverse of the gradient of the I – V curve.

RESISTIVITY

• The resistance of a material depends on

1. The type of material,

2. The length of the material, and

3. The cross sectional area of the material.

• The effect of the type of material on the

resistance of the material is known as the

resistivity of the material.

RESISTIVITY

• Definition: “The resistivity of a

material is numerically equal to the

resistance between the opposite

faces of a cube of the material, of

unit length and unit cross sectional

area. ”

RESISTIVITY

length of conductor, in m.

• How are the resistance of a wire and

resistivity of the wire’s material related

mathematically?

•��

where = resistance, in Ω; ρ

= resistivity, in Ωm; = cross

sectional area of the wire, in m2,

length of conductor, in m.

E X A M P L E S

H O M E W O R K

1. Oct/Nov 2008, Paper 1, question 32.1. Oct/Nov 2008, Paper 1, question 32.

H O M E W O R K

E L E C T R O M O T I V E F O R C E

( E M F )

( E M F )• To move charges around in a circuit, energy• To move charges around in a circuit, energy

must be transferred to the a unit charge tocause the charge to traverse the circuit.

• Definition: “The electromotive force (emf) isthe amount of change of other forms ofenergy, like chemical or mechanical intoelectrical energy per unit of charge.”

• “The emf can also be defined as the energytransferred by the source on a unit of chargeto drive the unit charge around the circuit.”

( E M F )

( E M F )• Diagram on the left shows an ideal

emf source

• �� is the electric force acting on the

positive charge produced by the E -

field.

• The non – electrostatic force, �� is

produced by an external source.

• In a battery / fuel cell, � is produced

by the chemical reactions that occur.

In a generator � is produced by the

magnetic forces that act on the

charges.

Diagram 25.13, page 829, Sear’s and Zemansky’s

University Physics, Young and Freedman, 13th edition,

Pearson Education, San Francisco, 2012.

( E M F )

( E M F )• Diagram shows what happens when

the ideal emf source is connected to

an external circuit.

• Let us assume that the positive

charge starts at point b, and is

moved to point a. The work done by

� ,�� "ε. Work done per unit

charge,��

• The work done per unit charge by

�� is the emf causing current to

Diagram 25.14, page 829, Sear’s and Zemansky’s

University Physics, Young and Freedman, 13th

edition, Pearson Education, San Francisco, 2012.

( E M F )

( E M F )• The charge gains electric potential

energy as it moves from b to a.

• The E – field that is produced by the

circuit will cause the charges to flow

(in the circuit) from a to b (higher to

lower potential)

• When the charges return to point b

after a completing a loop, the gain in

electric potential energy in moving

from b to a (in source) will have to

“dropped” across the circuit.

• Hence, & '(, where ' current

that flows, ( resistance of circuit.

( E M F )

( E M F )• The diagram shows an electric

source.

• A electric source has an internal

resistance, � between points b and

• This produces a lower potential

difference between a and b as

compared to the ideal source.

• �)* % + ��

• Hence, % �� , �� , ��

• Or, � %

��-��

Source: http://farside.ph.utexas.edu/teaching/302l/lectures/img635.png

( E M F )

( E M F )• For an electric source, the potential

difference across the terminals

would be equal to the emf only if

there is no current flowing through

the source.

• For example, a dry cell with an emf =

1.5 V would have a potential

difference = 1.5 V across the

terminals when I = 0. When current

flows, the potential difference across

the terminals would be less than 1.5

Source: http://farside.ph.utexas.edu/teaching/302l/lectures/img635.png

E X A M P L E S

May/Jun 2009, Paper 1, Question 32.

E X A M P L E S

Oct/Nov 2009, Paper 21, Question 6(cont’d).

E X A M P L E S

H O M E W O R K

1. May/June 2010, Paper 11, question 30.1. May/June 2010, Paper 11, question 30.

chapter 19 current of electricity

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