CH2 Basic Laws

ECE 276 1 Prof. Khalid Mirza

Chapter 2

Basic Laws

ECE 276 Electric Circuits


Resistivity

Materials tend to resist the flow of electricity through them

This property is called resistance

Variable Resistor / Potentiometer

Resistor


Ohms Law

R =

(passive sign convention)

Measured in ohms ( )


Shorts and Open Circuits

Short circuit A connection with almost zero resistance

Ideally, any current may flow through the short

Open circuit A connection with infinite resistance

No matter the voltage, no current flows


Conductance

Ability of an element to conduct electric current

=1

Measured in mhos ( ) or Siemens (S)


Linearity

Not all materials obey Ohms Law

Resistors that do are called linear resistors

Their current voltage relationship is always linearly proportional

Diodes and light bulbs are examples of non-linear elements


Power Dissipation

Running current through a resistor dissipates power

The power dissipated is a non-linear function of current or voltage

Power dissipated is always positive

A resistor can never generate power

22 vp vi i R

R


Nodes Branches and Loops Branch Single element (voltage src., resistor, etc.)

Node Pt. of connection b/w 2 or more branches

Loop Any closed path in a circuit

Branches =

Nodes =

Loops =

= +

R1

R3

R2

4

3

2

Node Node

Node

Loop Loop


Kirchoffs Laws Kirchoffs Current Law (KCL)

Algebraic sum of currents entering a node is zero

1

0N

n

n

i

1 2 + 3 + 4 5 = 0

(1 + 3 + 4) = (2 + 5)

Current entering

the node

Current leaving

the node


Kirchoffs Laws Kirchoffs Voltage Law (KVL)

Algebraic sum of all voltages around a loop is zero

1 2 3 + 4 5 = 0

(1 + 4) = (2 + 3 + 5)

Voltage

rises

Voltage

drops

1

0M

m

m

v


Series Resistors

R1 R2 RN

Req

= 1 + 2 ++ =

=0


Parallel Resistors

= 1 + 2 ++ =

=0

R2 RN Req R1 G2 GN G1 Geq

1

=1

1+1

2++

1

=

1

=0


Voltage Division

= 1 + 2 = i(1 + 2)

=

1 + 2

1 = 1 =11 + 2

2 = 2 =21 + 2

=

1 + 2 +


Current Division

= 1 + 2 =

1+

2

=121 + 2

1 =

1=21 + 2

2 =

2=11 + 2


Wye-Delta Transformations

There are cases where resistors are neither parallel nor series

Consider the bridge circuit


Wye-Delta Transformations

Two topologies can be interchanged:

Wye (Y) networks Delta () networks

Transforming between these two topologies often makes the solution of a circuit easier


Delta to Wye

1

2

3

b c

a b c

c a

a b c

a b

a b c

R RR

R R R

R RR

R R R

R RR

R R R


Wye to Delta

1 2 2 3 3 1

1

1 2 2 3 3 1

2

1 2 2 3 3 1

3

a

b

c

R R R R R RR

R

R R R R R RR

R

R R R R R RR

R


Active Elements Independent

Sources

Dependent Sources Source is controlled by

another voltage or current

4 types:

Voltage Source Current Source

Voltage

controlled

Current

controlled

Voltage

controlled

Current

controlled

CH2 Basic Laws

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