Download 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
Arizona State University
1
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
S’01
Introduction to Engineering II
Arizona State University
2
Ideal voltage source
Current-voltage characteristic
I
Circuit symbol
5V
ECE 194
S’01
Introduction to Engineering II
V
+
V
5V
Arizona State University
3
Ideal current source
Current-voltage characteristic
I
Circuit symbol
2A
V
ECE 194
S’01
Introduction to Engineering II
I
2A
Arizona State University
4
Connections of ideal sources
Valid connections
I2
2A
I1
2A
ECE 194
S’01
+
Introduction to Engineering II
VC1
5V
Arizona State University
+
VC0
5V
5
Connections of ideal sources
Invalid connections
IC1
5A
IC0
10 A
+
ECE 194
S’01
Introduction to Engineering II
VC1
5V
Arizona State University
+
VC0
2V
6
Connections of ideal sources
Valid or invalid?
VC1
5V
+IC0
10 A
ECE 194
S’01
Introduction to Engineering II
Arizona State University
7
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
ECE 194
S’01
Introduction to Engineering II
R1
1E3ž
Arizona State University
8
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
S’01
Introduction to Engineering II
Arizona State University
9
Electrical resistance, cont.
Example #1
R1
+ 1E3 ž
I
-
I = V/R = 5V/1E3W = 5mA
VC0
5V
+-
ECE 194
S’01
Introduction to Engineering II
Arizona State University
10
Electrical resistance, cont.
Example #2
R1
15 E3ž
What is voltage drop across R1
IC0
2E-3 A
ECE 194
S’01
Introduction to Engineering II
What is voltage polarity?
Arizona State University
11
Kirchhoff’s Laws
A node is a point in a circuit where two or more elements meet
R1
15 E3ž
R1
1E3 ž
R2
1E4 ž
IC5
5A
IC0
2E-3 A
ECE 194
S’01
R3
1E4 ž
R4
1E3 ž
IC0
2E-3 A
Introduction to Engineering II
Arizona State University
12
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
S’01
2
R2
1E4ž
I1 + I 2 + I 3 = 0
3
IC5
5A
Introduction to Engineering II
Arizona State University
13
Kirchhoff’s voltage law
The algebraic sum of all the voltages
around any closed path in a circuit equals zero
R1
1E3 ž
R2
1E4 ž
IC5
5A
R3
1E3 ž
VC4
5V
+
VC0
5V
VR3 + VR1 + VR2
+ VC0 + VC4 = 0
-+
ECE 194
S’01
Introduction to Engineering II
Arizona State University
14
Resistors in series
R1
10 ž
+
R3
20 ž
V1
30 V
Using KVL and KCL, we have:
-V1 + I*R1 + I*R2 = 0
I*(10 + 20) = 30 ---- I = 30V/30W = 1A
or
ECE 194
S’01
Introduction to Engineering II
Arizona State University
15
Resistors in series
This is equivalent to:
REQ
30 ž
+
Rs = R1 + R2
ECE 194
S’01
V1
30 V
Resistors in series add together
Introduction to Engineering II
Arizona State University
16
Resistors in parallel
+
V1
10 V
R1
10 0ž
R2
30 0ž
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
S’01
Introduction to Engineering II
Arizona State University
17
Resistors in parallel
This is equivalent to:
+
1/Rp = 1/R1 + 1/R2
ECE 194
S’01
RP
75 ž
V1
10 V
Resistors in parallel are
combined by adding their
reciprocals
Introduction to Engineering II
Arizona State University
18
Classwork
R1
4ž
+
V1
50 V
R2
80 ž
R3
20 ž
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
19