Transcript wire

Electric current
Electric Current
Thermal energy flows from
the hotter object to the
colder object.
Likewise, electrical energy is
transferred from areas with
higher potential to areas
with lower potential.
• Careful! NOT necessarily
individual charges
Quick rate of discharge
If you touch a Van der Graaf
generator with a wire also
connected to the ground,
the high potential of the
charged dome would very
quickly equalize with the
ground.
Shocking, but not always
super useful.
Recycling charge?
For most applications,
recycling charges
makes devices much
more useful.
To recycle charges, we
need the equivalent of
a pump somewhere in
the circuit.
Pumps for charges?
Charge only moves when
there is potential difference
Batteries
• chemical
 electrical
Generators
• mechanical
 electrical
We started the unit with
voltage for a reason!
Danger?
A Van der Graaf generator can build
up a potential difference of
20,000 J/C. It’s shocking to touch
but not typically dangerous.
A car battery maintains a potential
difference of just 12 J/C and will
seriously harm or kill you if you
complete the circuit with your body.
Check this from UC Denver Med School
Not the potential difference,
but the current!
Consider flow of water
About the same
potential difference
A romantic spot for a
swim with your special
someone
A disastrous spot for a
swim with anyone
Electric Current
• The flow of water is measured
in volume of water per unit
time.
• The flow of electricity
(current) is measured in
charge per second,
abbreviated as amperes or
amps.
Coulomb
second
I=Q/t
current = charge / time
= ampere or amp or A
Named in honor of Andre-Marie Ampere (1775 – 1836)
Example
In a certain light bulb, 3.0 C of charge pass through the filament
in 5.0 s. What is the current in the light bulb?
I=Q/t
Try =
it first.
3.0 C / 5.0 s
Move this box for the answer.
= 0.6 A
Example
The current in a light bulb is 0.8 A. How long does it take for
1.6 C of charge to pass a point in the wire?
I=Q/t
So,
t=Q/I
Try it first.
Move this box for the answer.
= 1.6 C / 0.8 A
= 20 s
Batteries
A battery uses chemical means to
cause charge to move continuously
through a circuit.
Alessandro Volta (1745 – 1827) invented
the battery (1800) and described the
work done by a battery per unit
charge as the ‘electromotive force’,
sometimes abbreviated emf and other
times  (lower case epsilon)
a problematic choice of
name, since it is not a
force
𝜀
𝑊
=
𝑞
𝐽
of
𝐶
has units
or volts
Graphing potential in a circuit
Suppose you connect a 9.0 V battery to a small motor. How
does the electric potential change in the circuit?
D
B
voltage
A
C
A
B
C
position
D
A
Graphing current in a circuit
D
Charge does NOT
get
used
up; the amount
A
going in must equal
the amount coming
C
B
out
current
Suppose you connect a 9.0 V battery to a small motor. How
does the current change in the circuit?
A
B
C
position
D
A
Graphing potential in a circuit
Suppose you connect a 9.0 V battery to two small motors in
series as shown below. How does the electric potential change
in the circuit?
E
A
B
D
C
voltage
F
A
B
C
position
D
E
F
Graphing current in a circuit
Suppose you connect a 9.0 V battery to two small motors in
series as shown below. How does the current change in the
circuit?
A
B
Charge does NOT get
used up; the amount
E
going in must equal
D
the amount coming
out
C
current
F
A
B
C
position
D
E
F
Comparison
In which situation would you expect the motor
to spin faster?
#1
#2
Graphing potential in a circuit
A
B
D
C
F
voltage
Suppose you connect a 9.0 V battery to two small motors in
parallel as shown below. How does the electric potential change
in the circuit?
A
E
B
C
position
D
A
Comparison 2
In which situation would you expect the motor
to spin faster?
#1
#2
Comparison 3
In which situation would you expect the battery
to run down faster?
#1
#2
Electric Power
Power is a measure of the
rate at which work is done.
𝑾
𝑷=
𝒕
In electric circuits, you can
calculate power by multiplying
how quickly charge flows by
the potential difference.
𝑷 = 𝑰𝑽
Power is measured in
joules per second.
𝐽
𝑠
is sometimes abbreviated
as watts, W
𝐶 𝐽 𝐽
x =
𝑠 𝐶 𝑠
Example
It takes about 2 minutes for an electric heater in the
US to bring 0.5 L of room-temperature water to a boil.
Estimate the power of the heater.
P=Q/t = mcT/t
Try it first.
= [(500 g) (4.2 J/gC)(100C-20C)]
Move this box for the answer.
/ 120 s
= 1,400 W
Estimate the current through the heater.
Note: most homes
in the US have potential difference of 120 V
Try it first.
P=IV,
so I = P / V = (1,400 J/s) / (120 J/C) = 12 A
Move this box for the answer.
Example
An electric heater draws a steady 15.0 A on a 120-V
line. How much power does it require?
PTry=itIfirst.
V = (15.0 C / s) (120 J / C) = 1800 W = 1.8 kW
Move this box for the answer.
Example
If an 1800-W electric heater operates 3.0 h per day and
operates for 30 days, how much does it cost to
operate? Assume that the electric company charges
$0.092 / kWh.
Cost = ($ / kWh) (kW) (h)
Try it first.
($0.092
/ kWh)
Move this=box
for the answer.
= $15
(1.8 kW) (3 h/day) (30 days)
Relationship between
voltage and current
 voltage   current
𝑉𝐼
Investigated by Georg Ohm,
a German physicist (1787 –
1854)
or
𝐼 = some proportionality constant 𝑉
𝐼 = ("conductance")𝑉
Conductance and Resistance
If conductance is a measure
of how easily current flows,
resistance is a measure of
how hard it is for current to flow.
1
1
𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 =
=
𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑅
𝐼 = ("conductance")𝑉
where 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 =
1
𝐼= 𝑉
𝑅
𝐼 =
𝑉
𝑅
1
𝑅
or 𝑉 = 𝑅𝐼 or 𝑅 =
𝑉
𝐼
Electrical Resistance
Electrical resistance is
potential difference
current
R =V / I
Resistance is measured in ohms
After Georg Ohm (1787 – 1854)
Units: V per A
= J / C per C / s
= J s / C2
Abbreviated with the Greek letter, omega, 
Ohm’s Law
• increase voltage  increase current
• increase resistance  decrease current
𝑽
𝑰=
𝑹
Check this link
http://phet.colorado.edu/sims/ohms-law/ohms-law_en.html
Example
A typical color television draws 2.5 A of current when connected
across a potential difference of 115 V. What is the resistance of
the television?
R =V / I
= 115 V / 2.5 A
Try it first.
Move this box for the answer.
= 46 
Example
A 1.5 V battery is connected to a small light bulb with a
resistance of 3.0 . What current will it draw?
I =V / R
= 1.5 V / 3.0 
Try it first.
Move this box for the answer.
= 0.5 A
Electric Power – pt 2
Since potential difference,V, is proportional to
current, I, and to resistance, R
𝑽 = 𝑰𝑹 and 𝑰 =
𝑽
𝑹
In electric circuits,
𝑷 = 𝑰 𝑰𝑹 = 𝑰𝟐 𝑹
𝑽
𝑽𝟐
𝑷=
𝑽=
𝑹
𝑹
Electrical Resistance
• The current in a river depends on
how quickly the water drops (potential
difference) and cross section of the
river.
• Likewise, the electrical current in a
conductor depends on the voltage
(potential difference) and the resistance.
Factors that affect
electrical resistance
• Length of conductor
 length   resistance
• Thickness of conductor
 cross-sectional area  resistance
• Type of material
 ‘grip’ on free electrons   resistance
Mathematical model
for resistance
𝒍
𝑹=𝝆
𝑨
 length, 𝒍   resistance
 cross-sectional area, 𝑨 
resistance
 grip on free electrons, 𝝆 
 resistance
Determined experimentally.
• Copper: 1.68 x 10-8 m
• Glass: 109 m
Varies with temperature!
Change in resistance 
change in voltage  use
electric current to measure
temperature
Example
Suppose you want to connect your stereo to remote speakers.
If each wire must be 20 m long, what diameter copper wire
should you use to keep the resistance less than 0.10  per wire?
Resistivity of copper is 1.68 x 10-8 m.
𝑙
𝑙
𝑅 = 𝜌 , so 𝐴 = 𝜌 𝑅, where A = r2 or 𝑟 = 𝐴/𝜋
𝐴
Try it first.
d = 2r = 2 𝜌𝑙/𝑅𝜋
Move this box for the answer.
= 2 (1.68 𝑥 10−8 𝑚)(20 𝑚)/(0.10)(𝜋)
= 0.0021 𝑚