Download INTRODUCTION - Foundation Coalition

Resistive Circuits

Resistors in series
Resistors in parallel
Voltage divider
Current divider
The bridge
S’01
Introduction to Engineering II
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ECE 194
Arizona State University
1
Electrical resistance
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
2
Resistors in series
R
R
R
1
R
2
n
T
RT  R1  R2  ...  Rn
ECE 194
S’01
Introduction to Engineering II
Arizona State University
3
Resistors in parallel
R
R
R
1
R
2
n
T
1
1 1
1
   ... 
RT R1 R2
Rn
ECE 194
S’01
Introduction to Engineering II
Arizona State University
4
Voltage divider
+
R
1
v
s
v
_
1
+
+
R
2
R1
v1  iR1  vs
R1  R2
v
2
_
vs  iR1  iR2
R2
v2  iR2  vs
R1  R2
vs
i
R1  R2
ECE 194
S’01
Introduction to Engineering II
Arizona State University
5
Current divider
+
I
s
v
I
1
R
1
I
2
R
2
v  i1 R1  i2 R2
_
R2
i1  i s
R1  R2
R1 R2
v  is R||  is
R1  R2
R1
i2  i s
R1  R2
ECE 194
S’01
Introduction to Engineering II
Arizona State University
6
A series-parallel connection
v
R
1
v
s
R
+
s
R + R
2
x
R + R
1
3
2
+
R
3
R
x
v
s
+
( R1+
R
3
) ( R2 +
R
x
)
R + R + R + R
1
3
2
x
ECE 194
S’01
Introduction to Engineering II
Arizona State University
7
The bridge
I
R
1
1
I
R
2
2
R2
Rx 
R3
R1
Am mete r
v
+
s
A
I
3
B
R
I
3
x
R
The bridge is “balanced”
when the ammeter reads zero
x
• If ammeter current = 0, I1 = I3 and I2 = Ix
• The points A and B are at the same potential
• So I3R3 = IxRx and I1R1 = I2R2
ECE 194
S’01
Introduction to Engineering II
Arizona State University
8
Classwork #1
20 ž
+
20 V
8ž
15ž
60 ž
10 ž
30 ž
18 ž
6ž
15 ž
48ž
10 ž
Find the total current emitted by the voltage source
ECE 194
S’01
Introduction to Engineering II
Arizona State University
9