1. Electric current
Physics 114
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Lecture V

2. 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

3. Concepts Primary concepts: Electric current Resistor and resistivity
Electric circuit
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4. Laws
Ohm’s law
Power in electric circuits
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5. Electric current - + A flow of charge is called an electric current
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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6. 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

7. 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.
Symbol for battery
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Lecture V

8. Electric circuit a). Will not work, Circuit is not closed
b). Will not work,
Circuit is at the same
potential (+), no potential difference - voltage.
c). Will work.
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Lecture V

9. Ohm’s law Electric current is proportional to voltage.
Coefficient in this dependence is called resistance R
Resistance is measured in Ohm (W = V/A) I R V
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10. Resistors First digit Second digit Multiplier Tolerance
2.5 x103 W +- 5%.
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11. Resistivity traffic  Electric current
Long narrow street  high resistance
Condition of the road  material property called resistivity r.
r is measured in W m
L – length of the conductor
A – its area.
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Lecture V

12. Resistance and Temperature
When electrons move through the conductor they collide with atoms:
Resistivity grows with temperature ( more collisions)
r0 – resistivity measured at some reference temperature T0
a – temperature coefficient of resistivity
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Lecture V

13. 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
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Lecture V

14. 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):
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Lecture V

15. Test problem
You have an open working refrigerator in your room. It makes your room
A hotter
B colder
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Lecture V

16. Test problem P=IV P=I2R P=V2/R
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 Brighter
B dimmer
P=IV P=I2R P=V2/R
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17. Alternating current (AC)
Voltage changes sign  current changes the direction I
Req ~
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18. Electric circuits: resistors
Current in=current out I1=I2
No electrons are lost inside
Resistors dissipate power (energy/time)
P=I2R
Drop of voltage over a resistor DV=-IR:
V2=V1-IR
I1,V1 R
I2,V2
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Lecture V

19. Electric circuits: wires
We assume that wire have very small resistance (R=0)
Current in=current out I1=I2
Power dissipated in wires
P=I2R=0
Drop of voltage over a resistor DV=-IR=0
V2=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
I1,V1
I2,V2
I1,V1
I2,V2
I1,V1
I2,V2
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Lecture V

20. Electric circuit: battery
Energy conservation
Drop of voltage in electric circuit is always equal to voltage supplied by an external source (e.g. battery).
Current (the effective flow of positive charge) goes from + to –
Electrons (negative charge!) go from – to + I R1 R2 R3 V
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21. Electric circuits: branches
Charge is conserved
Current – what goes in, goes out I1 I I2 I I3 V
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22. Symbols Circuits can be rearranged:
Wires with negligible resistance can be
Stretched
Bended
Collapsed to a point
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23. Skiing  electric circuita b
Ski lift c
Battery
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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24. 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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Lecture V

25. Parallel connection 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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26. DC circuits Series connection Parallel connection I=I1=I2=I3
V=V1+V2+V3
Req=R1+R2+R3
Parallel connection
I=I1+I2+I3
V=V1=V2=V3
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27. < < 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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28. 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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29. < < Series vs parallel - P R1=R2=R3=R Req=3R I=V/3R  Pnet=V2/3R
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