current flow and resistance previously in physics: we were concerned with forces between charges and...
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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 FLOW AND RESISTANCE
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.
CURRENT FLOW AND RESISTANCE
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?
CURRENT FLOW AND RESISTANCE
+Vb
Va
An Electric field. The field sets up an "electric potential" (voltage)
Negative charges fall into the potential
Positive charges get pushed away
CURRENT FLOW AND RESISTANCE
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.
--
-- +
--
-- +
CURRENT FLOW AND RESISTANCE
As the electrons are accelerated through the wire they collide with fixed particles (atoms) that deflect them, only to have them accelerate again.
- +
CURRENT FLOW AND RESISTANCE
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.
- +
CURRENT FLOW AND RESISTANCE
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.
CURRENT FLOW AND RESISTANCE
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.
CURRENT FLOW AND RESISTANCE
CURRENT FLOW AND RESISTANCE
t
EP
time
EnergyPower
CURRENT FLOW AND RESISTANCE
t
EP
time
EnergyPower
t
qEdP
CURRENT FLOW AND RESISTANCE
t
EP
time
EnergyPower
t
qEdP
Math trick #1:
CURRENT FLOW AND RESISTANCE
t
EP
time
EnergyPower
t
qEdP
Edt
qP
CURRENT FLOW AND RESISTANCE
t
qEdP
Edt
qP
CURRENT FLOW AND RESISTANCE
t
qEdP
Edt
qP
What’s (q/t)?
CURRENT FLOW AND RESISTANCE
t
qEdP
Edt
qP
EdIP
CURRENT FLOW AND RESISTANCE
t
qEdP
Edt
qP
EdIP
VIP
CURRENT FLOW AND RESISTANCE
VIP
1 Watt = 1 Amp x 1 Volt
CURRENT FLOW AND RESISTANCE
CURRENT FLOW AND RESISTANCE
EI
What is the relationship between I and E?
CURRENT FLOW AND RESISTANCE
What is the relationship between I and E?What about the dimensions of the conductor?
EI
CURRENT FLOW AND RESISTANCE
What is the relationship between I and E?What about the dimensions of the conductor?
EI
)(AreaEI
CURRENT FLOW AND RESISTANCE
EI
)(AreaEI
What is the relationship between I and E?What about the dimensions of the conductor?What about the conductor material?
CURRENT FLOW AND RESISTANCE
)(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”
CURRENT FLOW AND RESISTANCE
I
AreaE
AreaEI
)(
)(
Next is the first math ‘trick’…
CURRENT FLOW AND RESISTANCE
)(
)(
)(
AreaI
EI
AreaE
AreaEI
CURRENT FLOW AND RESISTANCE
)( AreaI
ENow we include some
Physics substitutions to include a more practical term, Voltage.
CURRENT FLOW AND RESISTANCE
)( AreaI
ENow we include some
Physics substitutions to include a more practical term, Voltage.
)( Area
I
dV
CURRENT FLOW AND RESISTANCE
)( AreaI
ENow we include some
Physics substitutions to include a more practical term, Voltage.
)( Area
I
dV
And now another math “trick”…
CURRENT FLOW AND RESISTANCE
)( AreaI
ENow we include some
Physics substitutions to include a more practical term, Voltage.
)( Area
I
dV
And now another math “trick”…
)(
)(
AreaId
V
CURRENT FLOW AND RESISTANCE
)(
)(
AreaId
V
So here we are…one final math ‘maneuver’…
CURRENT FLOW AND RESISTANCE
)(
)(
AreaId
V
So here we are…one final math ‘maneuver’…
)(
)(
Aread
VI
CURRENT FLOW AND RESISTANCE
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
CURRENT FLOW AND RESISTANCE
IRV So that: OHM'S LAW
Volts = (Amps) x (Ohms)
V = (A) x (
R
VVI
Ad
)(
Now we can write:
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