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ECE 276 1 Prof. Khalid Mirza
Chapter 2
Basic Laws
ECE 276 Electric Circuits
ECE 276 2 Prof. Khalid Mirza
Resistivity
Materials tend to resist the flow of electricity through them
This property is called resistance
Variable Resistor / Potentiometer
Resistor
ECE 276 3 Prof. Khalid Mirza
Ohms Law
R =
(passive sign convention)
Measured in ohms ( )
ECE 276 4 Prof. Khalid Mirza
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
ECE 276 5 Prof. Khalid Mirza
Conductance
Ability of an element to conduct electric current
=1
Measured in mhos ( ) or Siemens (S)
ECE 276 6 Prof. Khalid Mirza
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
ECE 276 7 Prof. Khalid Mirza
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
ECE 276 8 Prof. Khalid Mirza
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
ECE 276 9 Prof. Khalid Mirza
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
ECE 276 10 Prof. Khalid Mirza
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
ECE 276 11 Prof. Khalid Mirza
Series Resistors
R1 R2 RN
Req
= 1 + 2 ++ =
=0
ECE 276 12 Prof. Khalid Mirza
Parallel Resistors
= 1 + 2 ++ =
=0
R2 RN Req R1 G2 GN G1 Geq
1
=1
1+1
2++
1
=
1
=0
ECE 276 13 Prof. Khalid Mirza
Voltage Division
= 1 + 2 = i(1 + 2)
=
1 + 2
1 = 1 =11 + 2
2 = 2 =21 + 2
=
1 + 2 +
ECE 276 14 Prof. Khalid Mirza
Current Division
= 1 + 2 =
1+
2
=121 + 2
1 =
1=21 + 2
2 =
2=11 + 2
ECE 276 15 Prof. Khalid Mirza
Wye-Delta Transformations
There are cases where resistors are neither parallel nor series
Consider the bridge circuit
ECE 276 16 Prof. Khalid Mirza
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
ECE 276 17 Prof. Khalid Mirza
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
ECE 276 18 Prof. Khalid Mirza
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
ECE 276 19 Prof. Khalid Mirza
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
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