1. Announcements
Information you’d like to get from this course. Think of one or more things you’re curious about and would like to learn about in this course. Put them on a blank card I’ll supply. (For example, how does radio work? What is a carbon nanotube and how might one use it?) We’ll try to give you answers.
Since people in EE42 are supposed to take P/NP 1-unit EE43 we will not include a lab grade in the EE42 scoring. The new weights for grading in EE42 will be: MT1 22%; MT2 22%; HW 12%; Final 44%.
Homeworks – including the first one – will be due at 12:00 noon on Thursdays (not Wednesdays).
We’ll add some new lab sections; check the web site.
EE 42 and 100, Fall 2005
Week 1

2. Electric Charge
Definition: The quantity of electricity that flows in a given time or is held in a component such as a capacitor
Symbol: q
Unit: Coulomb (C)
Notes: Charges may be positive or negative
Like charges (e.g., + and +) repel each
other, unlike charges (+ and -) attract each
other
EE 42 and 100, Fall 2005
Week 1

3. Note: Current has polarity (flow direction).
Electric Current
Definition: rate of positive charge flow
Symbol: i
Units: Coulombs per second ≡ Amperes (A)
i = dq/dt
where q = charge (in Coulombs), t = time (in seconds)
Note: Current has polarity (flow direction).
EE 42 and 100, Fall 2005
Week 1

4. Note: Potential is always referenced to some point.
Electric Potential (Voltage)
Definition: energy per unit charge expended in moving a
charge from one place to another
Symbol: v
Units: Joules/Coulomb ≡ Volts (V)
v = dw/dq
where w = energy (in Joules), q = charge (in Coulombs)
Note: Potential is always referenced to some point. a
Subscript convention:
vab means the potential at a minus the potential at b.
vab ≡ va - vb b
EE 42 and 100, Fall 2005
Week 1

5. p = dw/dt = (dw/dq)(dq/dt) = vi
Electric Power
Definition: amount of energy transferred per unit
time
Symbol: p
Units: Joules per second ≡ Watts (W)
p = dw/dt = (dw/dq)(dq/dt) = vi
Concept:
As a positive charge q moves through a drop in voltage of amount v, it loses energy
energy change = qv
rate is proportional to # charges/sec
EE 42 and 100, Fall 2005
Week 1

6. The Ideal Basic Circuit Element
Polarity reference for voltage can be
indicated by plus and minus signs
Reference direction for the current
is indicated by an arrow
Examples: resistor, capacitor,
inductor, diode, … + v _
Attributes:
Two terminals (points of connection)
Cannot be subdivided into other elements
Mathematically described by its current-voltage
relationship
EE 42 and 100, Fall 2005
Week 1

7. A Note about Reference Directions
A problem like “Find the current” or “Find the voltage” is always accompanied by a definition of the direction:
- v + i
In this case, if the current turns out to be 1 mA flowing to the left, we would say i = -1 mA. (See prefixes in Hambley, p. 18.)
In order to perform circuit analysis to determine the voltages and currents in an electric circuit, you need to specify reference directions. There is no need to guess the reference direction so that the answers come out positive, however.
EE 42 and 100, Fall 2005
Week 1

8. Sign Convention Example
Suppose you have an unlabelled battery and you measure its voltage with a digital voltmeter (DVM). It will tell you the magnitude and sign of the voltage.
With this circuit, you are measuring vab.
The DVM indicates 1.401, so va is lower than vb by V.
Which is the positive battery terminal?
Note that we have used the “ground” symbol ( ) for the reference node on the DVM. Often it is labeled “C” for “common.”
EE 42 and 100, Fall 2005
Week 1

9. Sign Convention for Power
Passive sign convention
p = vi
p = -vi i i i i _ v + _ v + + v _ + v _
If p > 0, power is being delivered to the gray box.
If p < 0, power is being extracted from the box.
EE 42 and 100, Fall 2005
Week 1

10. Power Calculation Example
Find the power absorbed by each element:
Conservation of energy
 total power delivered
equals
total power absorbed
Aside: For electronics these are un-
realistically large currents – mA is
more typical than A (1 mA = 0.001A)
vi (W)
918
- 810
- 12
- 400
- 224
1116
p (W)
EE 42 and 100, Fall 2005
Week 1

11. Circuit Elements 5 ideal basic circuit elements:
voltage source
current source
resistor
inductor
capacitor
Many practical systems can be modeled with just sources and resistors
The basic analytical techniques for solving circuits with inductors and capacitors are the same as those for resistive circuits
active elements, capable of
generating electric energy
passive elements, incapable of
generating electric energy
EE 42 and 100, Fall 2005
Week 1

12. Electrical Sources
An electrical source is a device that is capable of converting non-electric energy to electric energy and vice versa.
Examples:
battery: chemical electric
dynamo (generator/motor): mechanical electric
Electrical sources can either deliver or absorb power
EE 42 and 100, Fall 2005
Week 1

13. Ideal Independent and Dependent Voltage Sources
Circuit element that maintains a prescribed voltage across its terminals, regardless of the current flowing in those terminals.
Voltage is known, but current is determined by the circuit to which the source is connected.
The voltage can be either independent of dependent on a voltage or current elsewhere in the circuit, and can be constant or time-varying.
Circuit symbols: _ vs
vs=m vx
vs=r ix + + +
independent
voltage-controlled
current-controlled
EE 42 and 100, Fall 2005
Week 1

14. Other Independent Voltage Source Symbols
Sinusoidal AC source
v(t) = Vpeaksin(wt)
(In US, veff = 120 V, so
Vpeak = 170 V)
Battery (realistic source) + VS
EE 42 and 100, Fall 2005
Week 1

15. EE 42 and 100, Fall 2005
Week 1

16. I-V Plot for a Real Battery
EE 42 and 100, Fall 2005
Week 1

17. Ideal Independent and Dependent Current Sources
Circuit element that maintains a prescribed current through its terminals, regardless of the voltage across those terminals.
Current is known, but voltage is determined by the circuit to which the source is connected.
The current can be either independent or dependent on a voltage or current elsewhere in the circuit, and can be constant or time-varying.
Circuit symbols: is
is=a vx
is=b ix
independent
voltage-controlled
current-controlled
EE 42 and 100, Fall 2005
Week 1

18. Electrical Resistance
Resistance: Electric field is proportional to current density, within a resistive material. Thus, voltage is proportional to current. The circuit element used to model this behavior is the resistor.
Circuit symbol:
Unit for R: Volts per Ampere ≡ ohms (W)
The current flowing in the resistor is proportional to the voltage across the resistor:
v = i R
where v = voltage (V), i = current (A), and R = resistance (W) R
(Ohm’s Law)
EE 42 and 100, Fall 2005
Week 1

19. Water analogies for electrical elements
Since you can’t see electricity, it is useful to think of the flow of
water as being like that of electric charge. We’ll see water
analogies for a number of electrical devices – capacitors, diodes,
etc.
Water analogy for charge: a quantity of water (say, 1 gallon is
like 1 coulomb of charge)
Water analogy for current flow: flow rate of water (say, 1 gallon
per second is like 1 coulomb per second = 1 ampere)
Electric potential difference (voltage) is like the difference in
pressure in a hydraulic system
The model for a resistor (an increased resistance reduces the current
that flows for a given voltage) is like the effect of putting a
sponge in a water pipe or crimping it
EE 42 and 100, Fall 2005
Week 1

20. Water Models for Currents and Resistors
EE 42 and 100, Fall 2005
Week 1

21. Resistance of an actual resistor
Material resistivity
= r (W-cm) T L W
Resistance = resistivity x length/(cross-sectional area)
R = r (L/WT)
EE 42 and 100, Fall 2005
Week 1

22. Electrical Conductance
Conductance is the reciprocal of resistance.
Symbol: G
Units: siemens (S) or mhos ( )
Example:
Consider an 8 W resistor. What is its conductance? W
EE 42 and 100, Fall 2005
Week 1

23. Short Circuit and Open Circuit
Wire (“short circuit”):
R = 0  no voltage difference exists
(all points on the wire are at the same potential)
Current can flow, as determined by the circuit
Air (“open circuit”):
R =   no current flows
Voltage difference can exist, as determined by the circuit
EE 42 and 100, Fall 2005
Week 1

24. Circuit Nodes and Loops
A node is a point where two or more circuit elements are connected.
A loop is formed by tracing a closed path in a circuit through selected basic circuit elements without passing through any intermediate node more than once
Example:
EE 42 and 100, Fall 2005
Week 1

25. Kirchhoff’s Laws Kirchhoff’s Current Law (KCL):
The algebraic sum of all the currents entering any node in a circuit equals zero. (An expression of the conservation of charge.)
Kirchhoff’s Voltage Law (KVL):
The algebraic sum of all the voltages around any loop in a circuit equals zero. (As a result of conservation of energy.)
EE 42 and 100, Fall 2005
Week 1

26. Note that p > 0 always, for a resistor.
Example: Power Absorbed by a Resistor
p = vi = ( iR )i = i2R
p = vi = v ( v/R ) = v2/R
Note that p > 0 always, for a resistor.
Example:
Calculate the voltage vg and current ia.
Determine the power dissipated in the 80W resistor.
EE 42 and 100, Fall 2005
Week 1

27. “Lumped Element” Circuit Modeling
(Model = representation of a real system which simplifies analysis)
In circuit analysis, important characteristics are grouped together in “lumps” (separate circuit elements) connected by perfect conductors (“wires”)
An electrical system can be modeled by an electric circuit (combination of paths, each containing 1 or more circuit elements) if the dimensions of the circuit are small compared with the wavelength of any electromagnetic waves in the vicinity (i.e., wavelength l = c/f >> physical dimensions of system, where c = velocity of EM waves and f = frequency of wave). For example, at 60 Hz, the powerline frequency in the U. S., l = 3 x 108 (m/s)/60 (1/s) = 5 x 106 m ~ 3000 miles! so we can do lumped element circuit modeling of ordinary circuits at 60 Hz.
EE 42 and 100, Fall 2005
Week 1

28. Construction of a Circuit Model
The electrical behavior of each physical component is of primary interest.
We need to account for undesired as well as desired electrical effects.
Simplifying assumptions should be made wherever reasonable.
EE 42 and 100, Fall 2005
Week 1

29. Terminology: Nodes and Branches
Node: A point where two or more circuit elements are connected
Branch: A path that connects two nodes
EE 42 and 100, Fall 2005
Week 1

30. Notation: Node and Branch Voltages
Use one node as the reference (the “common” or “ground” node) – label it with a symbol
The voltage drop from node x to the reference node is called the node voltage vx.
The voltage across a circuit element is defined as the difference between the node voltages at its terminals
Example:
– v1 + a R1 b + va _ + vb _ + vs R2 _ c
 REFERENCE NODE
EE 42 and 100, Fall 2005
Week 1

31. Using Kirchhoff’s Current Law (KCL)
Consider a node connecting several branches: i2 i3 i1 i4
Use reference directions to determine whether currents are “entering” or “leaving” the node – with no concern about actual current directions
EE 42 and 100, Fall 2005
Week 1

32. Alternative Formulations of Kirchhoff’s Current Law
(Charge stored in node is zero.)
Formulation 1:
Sum of currents entering node
= sum of currents leaving node
Formulation 2:
Algebraic sum of currents entering node = 0
Currents leaving are included with a minus sign.
Formulation 3:
Algebraic sum of currents leaving node = 0
Currents entering are included with a minus sign.
EE 42 and 100, Fall 2005
Week 1

33. EE 42 and 100, Fall 2005
Week 1

34. A Major Implication of KCL
KCL tells us that all of the elements in a single branch carry the same current.
We say these elements are connected in series.
Current entering node = Current leaving node
i1 = i2
EE 42 and 100, Fall 2005
Week 1

35. KCL Example Currents entering the node: -10 mA i
Currents leaving the node:
-10 mA i
5 mA
15 mA
3 formulations of KCL: 1. 2. 3.
EE 42 and 100, Fall 2005
Week 1

36. Generalization of KCL
The sum of currents entering/leaving a closed surface is zero. Circuit branches can be inside this surface, i.e. the surface can enclose more than one node! i2 i3
This could be a big chunk of a circuit, e.g., a “black box” i4 i1
EE 42 and 100, Fall 2005
Week 1

37. Generalized KCL Examples
50 mA
5mA
2mA i i
EE 42 and 100, Fall 2005
Week 1

38. Using Kirchhoff’s Voltage Law (KVL)
Consider a branch which forms part of a loop: – v2 + + v1 _
voltage
“drop”
voltage
“rise”
(negative drop)
loop
loop
Use reference polarities to determine whether a voltage is dropped – with no concern about actual voltage polarities
EE 42 and 100, Fall 2005
Week 1

39. Formulations of Kirchhoff’s Voltage Law
(Conservation of energy)
Formulation 1:
Sum of voltage drops around loop
= sum of voltage rises around loop
Formulation 2:
Algebraic sum of voltage drops around loop = 0
Voltage rises are included with a minus sign.
Formulation 3:
Algebraic sum of voltage rises around loop = 0
Voltage drops are included with a minus sign.
(Handy trick: Look at the first sign you encounter on each element when tracing the loop.)
EE 42 and 100, Fall 2005
Week 1

40. A Major Implication of KVL
KVL tells us that any set of elements that are connected at both ends carry the same voltage.
We say these elements are connected in parallel. + va _ + vb _
Applying KVL in the clockwise direction,
starting at the top:
vb – va = 0  vb = va
EE 42 and 100, Fall 2005
Week 1

41. KVL Example Three closed paths: v2 v3 +  1 2 +  va vb vc - 3 Path 1: vb v3 v2 - b a c
Path 1:
Path 2:
Path 3:
EE 42 and 100, Fall 2005
Week 1

42. An Underlying Assumption of KVL
No time-varying magnetic flux through the loop
Otherwise, there would be an induced voltage (Faraday’s Law)
Note: Antennas are designed to “pick up” electromagnetic waves; “regular circuits” often do so undesirably. 
Avoid these loops!
How do we deal with antennas (EECS 117A)?
Include a voltage source as the circuit representation of the induced voltage or “noise”.
(Use a lumped circuit model rather than a distributed (wave) model.)
EE 42 and 100, Fall 2005
Week 1

43. Resistors in Series
Consider a circuit with multiple resistors connected in series.
Find their “equivalent resistance”.
KCL tells us that the same current (I) flows through every resistor
KVL tells us I R1 R2
VSS  + R3 R4
Equivalent resistance of resistors in series is the sum
of the individual resistances
EE 42 and 100, Fall 2005
Week 1

44. Voltage Divider I = VSS / (R1 + R2 + R3 + R4) + – + – I R1 V1 R2 VSS + + – R3 V3 R4
EE 42 and 100, Fall 2005
Week 1

45. When can the Voltage Divider Formula be Used?+ – + – R2 V2 R2 V2  +  +
VSS
VSS R3 R3 R4 R4 R5 SS 4 3 2 1 V R × + = SS 4 3 2 1 V R × + ≠
Correct, if nothing else
is connected to nodes
because R5 removes condition
of resistors in series
EE 42 and 100, Fall 2005
Week 1

46. Resistors in Parallel
Consider a circuit with two resistors connected in parallel.
Find their “equivalent resistance”. x
KVL tells us that the
same voltage is dropped
across each resistor
Vx = I1 R1 = I2 R2
KCL tells us I1 I2
ISS R1 R2
EE 42 and 100, Fall 2005
Week 1

47. Equivalent conductance of resistors in parallel is the sum
General Formula for Parallel Resistors
What single resistance Req is equivalent to three resistors in parallel? +  V I R3 R2 R1
Req eq 
Equivalent conductance of resistors in parallel is the sum
EE 42 and 100, Fall 2005
Week 1

48. EE 42 and 100, Fall 2005
Week 1

49. Current Divider x Vx = I1 R1 = ISS Req I1 I2 ISS R1 R2
EE 42 and 100, Fall 2005
Week 1

50. Generalized Current Divider Formula
Consider a current divider circuit with >2 resistors in parallel: +  V
EE 42 and 100, Fall 2005
Week 1

51. Checklist of Terms Introduced
Charge, current, voltage, resistance, conductance, energy, power
Coulomb (C), ampere (A), volt (V), ohm (W), siemens (S) (mho), joule (J), watt (W)
Kirchhoff’s Current Law (KCL), Kirchhoff’s Voltage Law (KVL), Ohm’s Law
Series connection, parallel conncection
DC (steady), AC (time-varying)
Independent and dependent ideal voltage and current sources
EE 42 and 100, Fall 2005
Week 1