Transcript Circuit analysis - Foundation Coalition

Circuit Elements
ECE 194

Voltage and current sources

Electrical resistance

Kirchhoff’s Laws

Resistive Circuits
S’01
Introduction to Engineering II
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Voltage and current sources



An electrical source is a device that is capable of
converting nonelectric energy to electric energy
(and vice versa)
An ideal voltage source is a circuit element that
maintains a prescribed voltage across its terminals
regardless of current flowing in these terminals
An ideal current source is a circuit element that
maintains a prescribed current across its terminals
regardless of voltage across the terminals
ECE 194
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Introduction to Engineering II
Arizona State University
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Ideal voltage source
Current-voltage characteristic
I
Circuit symbol
5V
ECE 194
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Introduction to Engineering II
V
+
V
5V
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Ideal current source
Current-voltage characteristic
I
Circuit symbol
2A
V
ECE 194
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Introduction to Engineering II
I
2A
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Connections of ideal sources
Valid connections
I2
2A
I1
2A
ECE 194
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Introduction to Engineering II
VC1
5V
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+
VC0
5V
5
Connections of ideal sources
Invalid connections
IC1
5A
IC0
10A
+
ECE 194
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Introduction to Engineering II
VC1
5V
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+
VC0
2V
6
Connections of ideal sources
Valid or invalid?
VC1
5V
+IC0
10A
ECE 194
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Introduction to Engineering II
Arizona State University
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Electrical resistance
Resistance is the capacity of materials to impede the flow of current
A resistor is a circuit element that displays this behavior
I
Current-voltage characteristic
Circuit symbol
V
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Introduction to Engineering II
R1
1E3ž
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Electrical resistance, cont.
Resistor’s obey Ohm’s Law:
V=IR
The voltage “drop” across a resistor is linearly proportional
to the current passing through the resistor
ECE 194
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Introduction to Engineering II
Arizona State University
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Electrical resistance, cont.
Example #1
R1
+ 1E3 ž
I
-
I = V/R = 5V/1E3W = 5mA
VC0
5V
+-
ECE 194
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Introduction to Engineering II
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Electrical resistance, cont.
Example #2
R1
15E3 ž
What is voltage drop across R1
IC0
2E-3A
ECE 194
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Introduction to Engineering II
What is voltage polarity?
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Kirchhoff’s Laws
A node is a point in a circuit where two or more elements meet
R1
15E3 ž
R1
1E3ž
R2
1E4ž
IC5
5A
IC0
2E-3A
ECE 194
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R3
1E4ž
R4
1E3ž
IC0
2E-3A
Introduction to Engineering II
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Kirchhoff’s current law
The algebraic sum of all the currents
at any node in a curcuit equals zero
R1
1E3ž
I
I
1
I
ECE 194
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R2
1E4ž
I1 + I 2 + I 3 = 0
3
IC5
5A
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Kirchhoff’s voltage law
The algebraic sum of all the voltages
around any closed path in a circuit equals zero
R1
1E3ž
R2
1E4ž
IC5
5A
R3
1E3ž
VC4
5V
+
VC0
5V
VR3 + VR1 + VR2
+ VC0 + VC4 = 0
-+
ECE 194
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Introduction to Engineering II
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Resistors in series
R1
10ž
+
R3
20ž
V1
30V
Using KVL and KCL, we have:
-V1 + I*R1 + I*R2 = 0
I*(10 + 20) = 30 ---- I = 30V/30W = 1A
or
ECE 194
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Introduction to Engineering II
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Resistors in series
This is equivalent to:
REQ
30ž
+
Rs = R1 + R2
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V1
30V
Resistors in series add together
Introduction to Engineering II
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Resistors in parallel
+
V1
10V
R1
100 ž
R2
300 ž
Using KVL and KCL, we have:
I1 = 0.100A I2 = 0.033A
V1 = I1R1 = I2R2 = 10V
It = 0.100 + 0.033 = 0.133A
ECE 194
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Introduction to Engineering II
Arizona State University
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Resistors in parallel
This is equivalent to:
+
1/Rp = 1/R1 + 1/R2
ECE 194
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RP
75ž
V1
10V
Resistors in parallel are
combined by adding their
reciprocals
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Classwork
R1
4ž
+
V1
50V
R2
80ž
R3
20ž
Find (a) the current through R3, (b) the current
through R2, and (c) voltage across R1
ECE 194
S’01
Introduction to Engineering II
Arizona State University
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