EE 221 Review 1

• Basic components• Electric circuits• Voltage and current laws

Basics - SI base units

Base quantity Name Symbol

length meter m

mass kilogram kg

time second s

electric current ampere A

temperature kelvin K

Basics - SI prefixes

Factor Name Symbol Factor Name Symbol

10-18 atto a

10-15 femto f

10-12 pico p 1012 tera T

10-9 nano n 109 giga G

10-6 micro 106 mega M

10-3 milli m 103 kilo k

10-2 centi c

Basics - Charge

Two types of charge– positive: (proton)– negative: (electron, -1.6 10-19C)

Continuously transferring charge– total amount of charge never changed– neither created nor destroyed (conservation)

Defined in terms of ampereMeasured in coulomb (C) = As

t

tidttqtq

0

')()( 0

Basics - Current

Charge in motion– transfer of energy– related to charge

Representing current– numerical value (+ unit) (e.g., -13.5 A)– direction ( )– unit is the ampere (A)– represented by I, i, i(t)

Symbol for an independent current

source

Basics - Current

Example

(a,b) Incomplete, improper, and incorrect definitions of a current. (c) the correct definition of i1(t).

General, simple circuit element– two terminals– cannot be decomposed further– completely characterized by its

voltage-current relationship

Pushing charge– expenditure of energy– electrical voltage (potential difference)– voltage "across" the element

Basics - Voltage

A general two-terminalcircuit element

Voltage measures workrequired to move chargeRepresenting voltage– numerical value (+ unit) (e.g., -2.5 V)– direction (sense) ( + V - )

(left terminal is V volts positive withrespect to the right terminal)

– unit is volt (V = J / C)– represented by V, v, v(t)

Basics - Voltage

A general two-terminalcircuit element

Symbols: (a) DC voltage source;(b) battery; (c) ac voltage source.

Power is the rate of energyexpenditure: Voltage * Current– Voltage defined in terms of energy– Current is rate at which charge moves

Representing power– numerical value (+ unit) (e.g., -5.6 W)– "direction" by Passive Sign Convention– PSC: Current entering element through positive terminal– unit is watt (W = V *A = J / C *A = J / (As) *A = J / s)– represented by P, p, p(t)

Basics - Power

A general two-terminalcircuit element

Is a choice we make (convention)The current arrow is directedinto the "+" marked terminalThe power absorbed by the elementis given by the product p = v iA negative value indicates that poweris actually generatedOr: The power generated by theelement is given by the product p = - v i

Basics - Passive sign convention (PSC)

A general two-terminalcircuit element, p = vi represents the power absorbed

Resistance of conducting elementOhm's law: v = R i– linear, directly proportional

Passive elementPower p = v i = i2 R = v2 / RRepresenting resistance– numerical value (+ unit) (e.g., 3 )– unit is ohm ( = V / A)– represented by R

Basics - Resistor

NodesBranchesPathsLoops

Circuits

(a) A circuit containing three nodes and five branches.

(b) Node 1 is redrawn to look like two nodes; it is still one node.

Kirchhoff's current law

Conservation of charge

Circuits - KCL

The algebraic sum of the currentsentering any node is zero.

iA + iB - iC - iD = 0

Kirchhoff's voltage law

Conservation of energy

Circuits - KVL

The algebraic sum of the voltagesaround any closed path is zero.

v1 = v2 - v3

2

1 3

A B

C

+

-

+ -

-

+

v1

v2

v3

Circuits - Sources

(a) Series connected voltage sources can be replaced by a single source.

(b) Parallel current sources can be replaced by a single source.

Circuits - SourcesExamples of circuits with multiple sources, some of which are “illegal” as they violate Kirchhoff’s laws.

V-I Laws: Resistors

(a) Series combination of N resistors.

(b) Electrically equivalent circuit.

Req = R1 + R2 + ... + RN

V-I Laws: Resistors

(a) Parallel combination of N resistors.

(b) Electrically equivalent circuit.

1/Req = 1/R1 + 1/R2 + ... + 1/RN

A special case worth remembering is

Voltage division

Using KVL and Ohm's law to find v2.

An illustration of voltage division.

vRR

Rv

21

22

For a string of N series resistors ....

vRRR

Rv

N

kk

...21

Current division

Using KCL and Ohm's law to find i2.

iRR

Ri

21

12

For a parallel combination of N resistors

the current through Rk equals ....

i

RRR

Ri

N

kk 1

...11

1

21

An illustration of

current division.

Simplifying circuits (KVL)

V a+--

V b-+

R 1

v1

+ --

V c

V a+--

V b--+

R 1

+ --

V c

V 1+--

R 1

V 2--+

R 1

K VL

K VL

V1 = Va - Vb + Vc

V2 = -Va + Vb - Vc

• What do we count as positive?

• Direction of summation determines polarity

1st choice

2nd choice