CURRENT FLOW AND RESISTANCE Previously in Physics: we were concerned with forces between charges and...

CURRENT FLOW AND RESISTANCE

Previously in Physics: we were concerned with forces between charges and charges in electric fields.

Now we consider the motion of charges inside a conductor.

Electrons are loosely bound in conductors and move through the atomic structure easily.


CURRENT is the flow of charge and is defined as the amount of charge, q, that flows in time t, or:

t

qI

A 1

Amp 1

Ampere 1

Second

Coulomb 1

Back in the day, the international ampere was defined as the current that would deposit 0.001118 000 grams of silver per second from a solution of silver nitrate in water.

At present, it is defined as the amount of current which generates a force of two dynes per centimeter of length between two wires one centimeter apart.


In metallic conductors: electrons flow

In electrolytes (salt water): + and - ions flow

In a gas (neon, fluorescent): + and - ions, and electrons flow

What causes charges to move?


+Vb

Va

An Electric field. The field sets up an "electric potential" (voltage)

Negative charges fall into the potential

Positive charges get pushed away


If the electric field points in the same direction all the time, we get "DC", or direct current flow…a continual

flow of electrons in the same direction

If the electric field changes directions periodically then we get "AC", or alternating current…the electrons get

pulled back and forth, but make no net motion.

--

-- +

--

-- +


As the electrons are accelerated through the wire they collide with fixed particles (atoms) that deflect them, only to have them accelerate again.

- +


These collisions results in HEATING…which is why wires heat up if too much "current" flows through them

- +

As the electrons are accelerated through the wire they collide with fixed particles (atoms) that deflect them, only to have them accelerate again.

- +


So we write:

R

VI

The heating is due to "resistance" of the wire to the passage of the electrons. Different metals have different resistance to the flow of electrons.


IRV So that: OHM'S LAW

Volts = (Amps) x (Ohms)

V = (A) x (

So we write:

R

VI

The heating is due to "resistance" of the wire to the passage of the electrons. Different metals have different resistance to the flow of electrons.


t

EP

time

EnergyPower


t

EP

time

EnergyPower

t

qEdP


t

EP

time

EnergyPower

t

qEdP

Math trick #1:


t

EP

time

EnergyPower

t

qEdP

Edt

qP


t

qEdP

Edt

qP


t

qEdP

Edt

qP

What’s (q/t)?


t

qEdP

Edt

qP

EdIP


t

qEdP

Edt

qP

EdIP

VIP


VIP

1 Watt = 1 Amp x 1 Volt


EI

What is the relationship between I and E?


What is the relationship between I and E?What about the dimensions of the conductor?

EI


What is the relationship between I and E?What about the dimensions of the conductor?

EI

)(AreaEI


EI

)(AreaEI

What is the relationship between I and E?What about the dimensions of the conductor?What about the conductor material?


)(AreaE

I

EI

)(AreaEI

What is the relationship between I and E?What about the dimensions of the conductor?What about the conductor material?

= “resistivity”


I

AreaE

AreaEI

)(

)(

Next is the first math ‘trick’…


)(

)(

)(

AreaI

EI

AreaE

AreaEI


)( AreaI

ENow we include some

Physics substitutions to include a more practical term, Voltage.


)( AreaI



)( Area

I

dV


)( AreaI



)( Area

I

dV

And now another math “trick”…


)( AreaI



)( Area

I

dV

And now another math “trick”…

)(

)(

AreaId

V


)(

)(

AreaId

V

So here we are…one final math ‘maneuver’…


)(

)(

AreaId

V

So here we are…one final math ‘maneuver’…

)(

)(

Aread

VI


The term in the denominator is called the "Resistance"

= the resistivity of the material (look this up in a table)

d = distance, or length of the wire (“L” is often used)

A = the area of the wire (the cross-sectional area)

)( Aread

VI

)(resistance ohmsArea

dR


IRV So that: OHM'S LAW

Volts = (Amps) x (Ohms)

V = (A) x (

R

VVI

Ad

)(

Now we can write:

CURRENT FLOW AND RESISTANCE Previously in Physics: we were concerned with forces between charges and...

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