ECE 201, Section 3
Lecture 5
Prof. Peter Bermel
August 29, 2012
Recap from Monday
Kirchoff’s Current Law (KCL)
– Sum of all currents entering a node or Gaussian
surface is zero at all times:
= 0 ,forallt
Kirchoff’s Voltage Law (KVL)
– Voltage drop between any two nodes is directiondependent and path-independent (i.e., VAB =VA -VB )
– Sum of voltage drops over any closed loop is zero
8/29/2012
ECE 201-3, Prof. Bermel
Gaussian Surfaces
• Hypothetical surface through which sum of
currents must always be zero
• Clever choice of Gaussian surface can vastly
simplify problem
A
B
4A
C
• Example:
Io
12 A
D
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E
ECE 201-3, Prof. Bermel
6A
F
Series Resistive Circuits
• Calculate the effective resistance of N resistors in series:
R1
R2
2
1
• According to KVL:
4
3
, = ,
= = 8/29/2012
R4
R3
ECE 201-3, Prof. Bermel
5
Series Resistive Circuits
• Calculate the power dissipated by N resistors
in series
– For each element:
= – For the circuit as a whole:
=
= = 8/29/2012
ECE 201-3, Prof. Bermel
Parallel Resistive Circuits
• Given a current source Io connected to N parallel resistors, what is the
equivalent resistance?
I1
R1
I2
R2
I3
I4
R3
R4
• Equal voltage drop across every resistor implies:
= = • Kirchoff’s current law tells us that:
= =
= 8/29/2012
ECE 201-3, Prof. Bermel
Io
Parallel Resistive Circuits
• Calculate the power dissipated by N resistors
in parallel
– For each element:
= – For the circuit as a whole:
=
= = 8/29/2012
ECE 201-3, Prof. Bermel
Series-Parallel Circuits
• Combines features of series and parallel
circuits
• Depend on two reference points
• Solve iteratively with previous equations
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ECE 201-3, Prof. Bermel
Series-Parallel Circuits
R5
• Example:
R2
R1
1
R3
R4
2
Equivalent resistance across source terminals:
1
1
1
=
+
+ !"
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=
#
+
$ $%
ECE 201-3, Prof. Bermel
Io
Summary
• Series resistors:
= = / ; currents equal
• Parallel resistors
= = / ; voltages equal
• Series-parallel circuits
– Analyzed iteratively
8/29/2012
ECE 201-3, Prof. Bermel
Loading Effect
• Measuring voltage requires using a large but
finite resistance
200 Ω
• Example:
– 1.25 V nominal
– 1.21 V measured
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+
1.5 V
-
ECE 201-3, Prof. Bermel
+
1 kΩ
5 kΩ
-
Internal Resistance
• Internal resistance distinguishes real battery
from ideal battery
• Would like internal resistance to be as low as
possible
• Example:
5 mΩ
– 1.5 V nominal
– 1.48 V measured
– 80 mW heat loss
8/29/2012
+
+
ECE 201-3, Prof. Bermel
1.5 V
4A
-
Internal Resistance
• Another example:
– Current source
– 1.5 V load
– 1 A nominal
– 0.97 A measured
– 45 mW heat loss
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+
1A
50 Ω
-
ECE 201-3, Prof. Bermel
Voltage Sources
• Ideal voltage source:
+
+
-
V
V=Vs
I
Vs
I
-
• Non-ideal voltage source:
R
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V=Vs-IR
+
+
V
I
Vs
I
Note: R is generally small
ECE 201-3, Prof. Bermel
Ideal Current Sources
• Ideal current source
+
V
Is
I=Is
I
-
• Non-ideal current source:
+
Is
I=Is-V/R
R
I
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V
Note: R is generally large
ECE 201-3, Prof. Bermel
Homework
• HW #3 solution now posted
• HW #4 due today by 4:30 pm in EE 325B
• HW #5 due Friday: DeCarlo & Lin, Chapter 2:
– Problem 25
– Problem 32(b)
– Problem 35
– Problem 41
8/29/2012
ECE 201-3, Prof. Bermel