Electric current
Physics 114
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Lecture V
1
Up to this point
• Static situation – charges are not moving
– Coulombs force = charge * electric field
– Deeper look in the properties of the electric field Gauss’s law
– Potential energy= charge * electric potential
– Electric potential – integral of electric field
– Electric field = gradient of the electric potential
• Next – dymanics = moving charges = electric
current
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Lecture V
2
Concepts
• Primary concepts:
– Electric current
– Resistor and resistivity
– Electric circuit
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Laws
• Ohm’s law
• Power in electric circuits
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Electric current
• A flow of charge is called an
electric current
I  Q / t
Note: net charge =0
• It is measured in ampere
(A=C/s)
• Need free charge to have
electric current. Use
conductors.
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+
+
+
+
+
+
Lecture V
+
5
Skiing  electric circuit
High PE
High PE
Low PE
Low PE
Skiers
Charges
go from points with high PE to low PE
To complete the circuit need a device that brings you back
to high PE:
Ski lift
Battery
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Lecture V
6
Electric circuit
• Need free charge  electric circuit must consist of
conductive material (wires).
• Electric circuit must be closed.
• Battery supplies constant potential difference –
voltage.
e-
•Battery converts
chemical energy into
electric energy.
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Lecture V
Symbol for battery
7
Electric circuit
a). Will not work,
Circuit is not
closed
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b). Will not work,
Circuit is at the same
potential (+), no
potential difference voltage.
Lecture V
c). Will work.
8
Ohm’s law
• Electric current is proportional to voltage.
I V
V  IR
• Coefficient in this dependence
is called resistance R
I
• Resistance is measured in
Ohm (W = V/A)
R
V
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Lecture V
9
Resistors
•
•
•
•
•
First digit
Second digit
Multiplier
Tolerance
2.5 x103 W +- 5%.
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Lecture V
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Resistivity
• traffic
 Electric current
• Long narrow street  high resistance
• Condition of the road  material property called
resistivity r.
L
Rr
A
r is measured in W m
L – length of the conductor
A – its area.
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Lecture V
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Resistance and Temperature
• When electrons move through the conductor they
collide with atoms:
– Resistivity grows with temperature ( more collisions)
r  r0 (1   (T  T0 ))
r0 – resistivity measured at some reference temperature T0
 – temperature coefficient of resistivity
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Lecture V
12
Resistance and Temperature
• When electrons move through the conductor they
collide with atoms:
– Temperature of the conductor increases because of the
current (through collisions)
– Electrical energy is transformed into thermal energy
– Resistors dissipate energy
– Power – energy per unit of time- (in W=J/s) dissipated by a
resistor
PI R
2
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Lecture V
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Electric power
• Electric energy can be
converted into other
kinds of energy:
–
–
–
–
Thermal ( toaster)
Light (bulbs)
Mechanical (washer)
Chemical
• Electric power (energy
per unit of time):
P  IV
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Lecture V
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Test problem
• You have an open working refrigerator in your
room. It makes your room
–A
–B
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hotter
colder
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15
Test problem
• A light bulb is connected to a battery. It is then
cooled and its resistance decreased. Brightness is
proportional to consumed power. The light bulb
burns
–A
–B
P=IV
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Brighter
dimmer
P=I2R
Lecture V
P=V2/R
16
Alternating current (AC)
• Voltage changes sign  current changes the direction
V  V0 sin t
I  I 0 sin t
Vrms  V0 / 2
I rms  I0 / 2
PI
2
rms
R V
2
rms
/R
I 0  V0 / Req
I
Req
~
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Lecture V
V0 sin t
17
Electric circuits: resistors
• Current in=current out I1=I2
– No electrons are lost inside
• Resistors dissipate power
(energy/time)
I1,V1
R
I2,V2
– P=I2R
• Drop of voltage over a
resistor V=-IR:
– V2=V1-IR
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Electric circuits: wires
• We assume that wire have
very small resistance (R=0)
• Current in=current out I1=I2
• Power dissipated in wires
I1,V1
I2,V2
– P=I2R=0
• Drop of voltage over a resistor
V=-IR=0
– V2=V1
I1,V1
• From the point of electric
circuit wires can be
– stretched,
– Bended
– Straightened
– Collapsed to a point
without changing the electrical
properties of the circuit
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I1,V1
Lecture V
I2,V2
I2,V2
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Electric circuit: battery
Vbattery  V  IR1  IR2  IR3
• Drop of voltage in electric circuit
is always equal to voltage
supplied by an external source I
(e.g. battery).
• Current (the effective flow of
positive charge) goes from + to –
• Electrons (negative charge!)
go from – to +
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Lecture V
R1
R2
R3
V
20
Electric circuits: branches
• Charge is conserved
• Current – what goes in, goes out
I1
I  I1  I 2  I 3
I
I2
I
I3
V
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Symbols
• Circuits can be
rearranged:
– Wires with negligible
resistance can be
– Stretched
– Bended
– Collapsed to a point
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Lecture V
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Skiing  electric circuit
a
b
c
Cannot stop at b, must get to c –
ski lift:
V=V1+V2 - Net voltage drop in a
circuit is always equal to the
supplied voltage (e.g. battery)
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Series connection
• Charge conservation:
– I=I1=I2=I3
• Ohm’s law
– V1=IR1; V2=IR2; V3=IR3
• Energy conservation:
– qV=qV1+qV2+qV3
– V=V1+V2+V3
• IReq=IR1+IR2+IR3
• Req=R1+R2+R3
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Parallel connection
1
1
1
1
 

Req R1 R2 R3
• Charge conservation: I=I1+I2+I3
• Energy conservation: V=V1=V2=V3
• Ohm’s law: I1=V/R1; I2=V/R2; I3=V/R3
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Lecture V
V
V V V
 

Req R1 R2 R3
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DC circuits
•
•
•
•
Series connection
I=I1=I2=I3
V=V1+V2+V3
Req=R1+R2+R3
• Parallel connection
• I=I1+I2+I3
• V=V1=V2=V3
• 1  1  1  1
Req
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Lecture V
R1
R2
R3
26
Series vs parallel - I
•
•
•
•
R1=R2=R3=R
Req=3R
I=V/(3R)
I1=I2=I3=I=V/(3R)
<
<
•
•
•
•
R1=R2=R3=R
Req=R/3
I=3V/R
I1=I2=I3=I/3=V/R
Total current and individual currents are smaller in series connection.
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Series vs parallel - Req
• R1=R2=R3=R
• Req=3R
>
• R1=R2=R3=R
• Req=R/3
Equivalent resistance is larger in series connection.
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Series vs parallel - P
P1=I2R
Pnet=IV
Brightness
proportional
to power
•
•
•
•
R1=R2=R3=R
Req=3R
I=V/3R  Pnet=V2/3R
I1=V/3R P1=V2/9R
<
<
•
•
•
•
R1=R2=R3=R
Req=R/3
I=3V/R  Pnet=3V2/R
I1=V/R  P1=V2/R
Total and individual power consumptions are smaller in series connection.
Light bulbs are brighter in parallel connection.
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Lecture V
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