1. DC Circuits
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2. Examples of Circuits
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3. Current: Flow Of Charge
 Q t
Average current Iav: Charge Q flowing across area A in time t I av
Instantaneous current: differential limit of Iav
I  dQ dt
Units of Current: Coulombs/second = Ampere
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4. Direction of The Current
Direction of current is direction of flow of pos. charge
or, opposite direction of flow of negative charge
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5. Clicker question 1

6. J  I Iˆ Iˆ points in direction of current � �
Current Density J
J: current/unit area �
J  I Iˆ A
Iˆ points in direction of current
� �
I   J  nˆ dA  J  dA
S S
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7. Why Does Current Flow?
If an electric field is set up in a conductor, charge will move (making a current in direction of E).
Negative charges will move opposite to E’s direction, The resulted current is still in the same direction as E.
Note that when current is flowing, the conductor is not an equipotential surface (and Einside ≠ 0)!
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8. Microscopic Picture
Drift speed is velocity forced by applied electric field in the presence of collisions.
It is typically 4x10-5 m/sec, or 0.04 mm/second!
To go one meter at this speed takes about 10 hours!
How Can This Be?
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9. Conductivity and Resistivity
Ability of current to flow depends on density of charges & rate of scattering
Two quantities summarize this:
: conductivity
: resistivity

10.   1 � � � � J   E or E  J or  Microscopic Ohm’s Law
� � � �
J   E or E  J or
  1 
 and  depend only on the microscopic properties of the material, not on its shape
If current density j is uniform and perpendicular to the cross-section area, I=jA

11. Temperature Effects on 
For metals, the resistivity is extremely low, because there are a lot of free charges. The resistivity linearly increases with increasing temperature over a large range of T: Because at higher T, the free charges will be blocked more by the active lattices of atoms.
Semiconductors, such as silicon, have little free charges. When temperature increases, more electrons can be set free, hence the conductivity increases and resistivity decreases.

12. PRS Questions: Resistance?

13. Why Does Current Flow?
Instead of thinking of Electric Field, think of potential difference across the conductor

15. Ohm’s Law
V IR
I=DV/R; Current is determined by the potential difference DV and the resistance R between any two points.
R= DV/I; The electrical resistance of a circuit component is the potential difference DV between its ends divided by the current I, that is established in response to the potential difference.
R  kL A
R has units of Ohms () = Volts/Amp

16. P  I V Electrical Power P  d U  d qV   dq V dt dt dt
Power is change in energy per unit time
So power to move current through circuit elements:
P  d U  d qV   dq V dt dt dt
P  I V

17. Power - Battery Psupplied  I V  I 
Moving from the negative to positive terminal of a battery increases your potential. If current flows in that direction the battery supplies power I
Psupplied  I V  I 

18. Power - Resistor
Moving across a resistor in the direction of current decreases your potential.
Resistors always dissipate power whenever there is current and convert electrical potential energy into heat.
This is also called Ohmic losses or Joule heating.

19. Power - Resistor
When the potential drop across the resistor, DV, is fixed, the rate of Joule heating is reversely proportional to R.
When the current through the resistor, I, is fixed, the rate of Joule heating is proportional to R.
Please notice that regular metal wires has very little resistance comparing to the actual resistors we use in a circuit. In general, we consider there is no resistance and voltage drop in wires, even when a current flows.

20. PRS Questions: More Light Bulbs

21. Symbols for Circuit Elements
Battery
Resistor
Capacitor
Switch

22. Sign Conventions - Battery
Moving from the negative to positive terminal of a battery increases your potential
V  Vb Va
Think: Ski Lift

23. Sign Conventions - Resistor
Moving across a resistor in the direction of current
decreases your potential
V  Vb Va
Think: Ski Slope

24. Sign Conventions - Capacitor
Moving across a capacitor from the negatively to positively charged plate increases your potential
V  Vb Va
Think:
Ski Lodge

25. Series vs. Parallel
Series
Parallel

26. Req V  I R1  I R2  I (R1  R2 )  I Req  R1  R2
Resistors In Series
The same current I must flow through both resistors
V  I R1  I R2  I (R1  R2 )  I Req
Req
 R1  R2

27. Req Resistors In Parallel R1 R2 Req 1  1  1 R1 R2
Voltage drop across the resistors must be the same
V  V1  V2  I1R1  I2 R2  IReq
V V V
R1 R2 Req
1  1  1
I  I1  I2   
Req
R1 R2

28. PRS Questions: More Light Bulbs