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Schedule…. Divided We Fall. Matthew 12:25-26 25 And Jesus knew their thoughts, and said unto them, Every kingdom divided against itself is brought to desolation; and every city or house divided against itself shall not stand: Nephi 7:2 - PowerPoint PPT PresentationTRANSCRIPT
Discussion #5 – Ohm’s LawECEN 301 1
Date Day ClassNo.
Title Chapters HWDue date
LabDue date
Exam
17 Sept Wed 5 Ohm’s Law 2.6
18 Sept Thu LAB 1
19 Sept Fri Recitation HW 2
20 Sept Sat
21 Sept Sun
22 Sept Mon 6 Things Practical 2.6 – 2.8
LAB 2
23 Sept Tue
24 Sept Wed 7 Network Analysis 3.1 – 3.2
Schedule…
Discussion #5 – Ohm’s LawECEN 301 2
Divided We FallMatthew 12:25-26 25 And Jesus knew their thoughts, and said unto them,
Every kingdom divided against itself is brought to desolation; and every city or house divided against itself shall not stand:
Nephi 7:2 2 And the people were divided one against another; and
they did separate one from another into tribes, every man according to his family and his kindred and friends; and thus they did destroy the government of the land.
Discussion #5 – Ohm’s LawECEN 301 3
Lecture 5 – Resistance & Ohm’s Law
Discussion #5 – Ohm’s LawECEN 301 4
Open and Short Circuits
Short circuit: a circuit element across which the voltage is zero regardless of the current flowing through itResistance approaches zeroFlow of current is unimpededex: an ideal wire
• In reality there is a small resistance i
R = 0v = 0v
+
–
Discussion #5 – Ohm’s LawECEN 301 5
Open and Short Circuits
Undesirable short circuit – accidental connection between two nodes that are meant to be at different voltages. The resulting excessive current causes: overheating, fire, or explosion
Discussion #5 – Ohm’s LawECEN 301 6
Open and Short Circuits
Open circuit: a circuit element through which zero current flows regardless of the voltage applied to itResistance approaches infinityNo current flowsex: a break in a circuit
• At sufficiently high voltages arcing occurs i
R ∞i = 0v
+
–
Discussion #7 – Node and Mesh Methods
ECEN 301 7
Open and Short Circuits
i2+v2
–
vs+_
+v3
–
+ v1 –
R2
R1
R3
i3i1
Example: What happens to R2 and R3 if R1 is shorted? Vs = 2V, R1 = 2Ω, R2 = R3 = 4Ω, i1 = 500mA
R2 and R3 = ¼ W rating, R1 = ½ W rating
Discussion #7 – Node and Mesh Methods
ECEN 301 8
Open and Short Circuits
Example: What happens to R2 and R3 if R1 is shorted? Vs = 2V, R1 = 2Ω, R2 = R3 = 4Ω, i1 = 500mA
R2 and R3 = ¼ W rating, R1 = ½ W rating
i2+v2
–
vs+_
+v3
–
+ v1 –
R2
R1
R3
i3i1
V
mA
Riv
1
2500111
V
vvv
vvvs
1
0
122
21
mA
R
vi
2504
12
22
Discussion #7 – Node and Mesh Methods
ECEN 301 9
Open and Short Circuits
i2+v2
–
vs+_
+v3
–
+ v1 –
R2
R1
R3
i3i1
W
mW
VmA
viP
2
1
500
1500111
Example: What happens to R2 and R3 if R1 is shorted? Vs = 2V, R1 = 2Ω, R2 = R3 = 4Ω, i1 = 500mA
R2 and R3 = ¼ W rating, R1 = ½ W rating
W
mW
VmA
viP
4
1
250
1250222
Discussion #7 – Node and Mesh Methods
ECEN 301 10
Open and Short Circuits
i2+v2
–
vs+_
+v3
–R2
R3
i3i1
Example: What happens to R2 and R3 if R1 is shorted? Vs = 2V, R1 = 2Ω, R2 = R3 = 4Ω, i1 = 500mA
R2 and R3 = ¼ W rating, R1 = ½ W rating
V
vv
vv
s
s
2
0
2
2
mA
R
vi
5004
22
22
W
VmA
viP
1
2500222
BAD! R2 and R3 are damaged
Discussion #5 – Ohm’s LawECEN 301 11
Series Resistors Series Rule: two or more circuit elements are said to
be in series if the current from one element exclusively flows into the next element. From KCL: all series elements have the same current
N
nnEQ RR
1
R1
∙ ∙ ∙ ∙ ∙ ∙R2 R3 Rn RN
REQ
Discussion #5 – Ohm’s LawECEN 301 12
Series Resistors Demonstration of series rule: apply KVL and
Ohm’s law on the circuit
i
VR
Ri
RRRi
RiRiRi
vvvV
vvvV
sEQ
EQ
s
s
)(
)()()(
0
321
321
321
321
Vs
+_
+ v1 –
R1
– v3 +
R3
R2
+v2
–
1.5V
i
Discussion #5 – Ohm’s LawECEN 301 13
Series Resistors Voltage divider: the voltage across each resistor in a
series circuit is directly proportional to the ratio of its resistance to the total series resistance of the circuit
NB: the ratio will always be <= 1
EQ
n
R
R
sEQ
n
sNn
nn
VR
R
VRRRRR
Rv
321
Discussion #5 – Ohm’s LawECEN 301 14
Series Resistors Voltage divider: the voltage across each resistor in
a series circuit is directly proportional to the ratio of its resistance to the total series resistance of the circuit
sEQ
VR
Rv 1
1 Vs
+_
+ v1 –
R1
– v3 +
R3
R2
+v2
–
1.5V
i
sEQ
VR
Rv 2
2 sEQ
VR
Rv 3
3
Discussion #5 – Ohm’s LawECEN 301 15
Series Resistors
Example1: Determine v3
Vs = 3V, R1 = 10Ω, R2 = 6Ω, R3 = 8Ω
Vs
+_
– v1 +
R1
+ v3 –
R3
R2
+v2
–
i
Discussion #5 – Ohm’s LawECEN 301 16
Series Resistors
Example1: Determine v3
Vs = 3V, R1 = 10Ω, R2 = 6Ω, R3 = 8Ω
V
V
V
s
1
324
8
R
R v
:Divider oltage Using
EQ
33
Vs
+_
– v1 +
R1
+ v3 –
R3
R2
+v2
–
i
24
8610
:Rule Series Using
321 RRRREQ
Discussion #5 – Ohm’s LawECEN 301 17
Parallel Resistors Parallel Rule: two or more circuit elements are said to
be in parallel if the elements share the same terminalsFrom KVL: the elements will have the same voltage
N
EQNEQ
RRRR
RRRRRR 1111
111111
321
321
+R1
–
+R2
–
+R3
–
+Rn
–
+RN
–
+REQ
–
NB: the parallel combination of two resistors is often written: R1 || R2
Discussion #5 – Ohm’s LawECEN 301 18
Parallel Resistors Demonstration of parallel rule: apply KCL and
Ohm’s law on the circuit
i1 i2 i3
+R1
–
is+R2
–
+R3
–
+
v
–
Node a
sEQ
EQ
s
s
i
vR
Rv
RRRv
R
v
R
v
R
v
iiii
iiii
1
111
0
:a nodeat KCL
321
321
321
321
Discussion #5 – Ohm’s LawECEN 301 19
Parallel Resistors Current divider: the current in a parallel circuit divides in
proportion to the resistances of the individual parallel elements
sn
EQ
s
EQ
n
s
Nn
nn
iR
R
i
R
R
i
RRRRR
Ri
1
1
11111
1
321
NB: the ratio will always be <= 1 n
EQ
R
R
Discussion #5 – Ohm’s LawECEN 301 20
Parallel Resistors Current divider: the current in a parallel circuit
divides in proportion to the resistances of the individual parallel elements
sEQ
sEQ
iR
R
iR
Ri
1
11 /1
/1
sEQ i
R
Ri
22
sEQ i
R
Ri
33
i1 i2 i3
+R1
–
is+R2
–
+R3
–
NB: it makes sense that the smaller the resistor, the larger the amount of current that will flow.
Discussion #5 – Ohm’s LawECEN 301 21
Parallel Resistors
Example2: find i1R1 = 10Ω, R2 = 2 Ω, R3 = 20 Ω, Is = 4A
i1 i2 i3
–R1
+
is–
R2
+
–R3
+
Discussion #5 – Ohm’s LawECEN 301 22
Parallel Resistors
Example2: find i1R1 = 10Ω, R2 = 2 Ω, R3 = 20 Ω, Is = 4A
13
2020
11021
201
21
101
1
1111
terminalsshare elements all :
321 RRR
REQ
NB
i1 i2 i3
–R1
+
is–
R2
+
–R3
+
A
i
R
R i s
EQ
615.065
40
4
2013101
1
1
:dividercurrent Using
11
Discussion #5 – Ohm’s LawECEN 301 23
Parallel Resistors
Example2: find i1R1 = 10Ω, R2 = 2 Ω, R3 = 20 Ω, Is = 4A
s
EQ
EQs
EQs
sEQ
sEQ
sEQ
s
s
i
R
Ri
R
RRRi
iR
Ri
R
Ri
R
R
iiii
iiii
/1
/1
/1
/1/1/1
/1
/1
/1
/1
/1
/1
0
:dividingcurrent with holds KCLt Verify tha
321
321
321
321
i1 i2 i3
–R1
+
is–
R2
+
–R3
+
Discussion #5 – Ohm’s LawECEN 301 24
Parallel Resistors The parallel combination of resistors is often written:
For two resistors: R1 || R2
For three resistors: R1 || R2 || R3 etc.
In each case REQ for the parallel combination must be found
213132
321
321
213132
321
321
1
1111
||||
RRRRRR
RRR
RRRRRRRRR
RRR
RRR
12
21
21
12
21
21
1
111
||
RR
RR
RRRR
RR
RR
+R1
–
+R2
–
+R3
–
+R1
–
+R2
–
+R1|| R2|| R3
–
+R1|| R2
–
Discussion #5 – Ohm’s LawECEN 301 25
Parallel Resistors Example3: find v
vs = 5V, R1 = 1kΩ, R2 = 1kΩ
is
+R2
–
vs+_
+R3
–
+ R1 –
+
v
–
Discussion #5 – Ohm’s LawECEN 301 26
Parallel Resistors Example3: find v
vs = 5V, R1 = 1kΩ, R2 = 1kΩ
is
+R2
–
vs+_
+R3
–
+ R1 –
+
v
–
isR2 || R3
vs+_
+ R1 –
+
v
–
Discussion #5 – Ohm’s LawECEN 301 27
Parallel Resistors Example3: find v
vs = 5V, R1 = 1kΩ, R2 = 1kΩ
isR2 || R3
vs+_
+ R1 –
+
v
–
s
s
s
s
s
sEQ
vRRRRRR
RR
vRRRRRR
RR
RR
RR
v
RRRRRRRRRR
RR
v
RRRR
RRR
RR
vRRR
RR
vR
RRv
)(
)()(
1
1
)||(
||
||
:divider voltage Using
323121
32
323121
32
32
32
32
32312132
32
32
321
32
32
321
32
32
Discussion #5 – Ohm’s LawECEN 301 28
Parallel Resistors Example3: find v
vs = 5V, R1 = 1kΩ, R2 = 1kΩ
isR2 || R3
vs+_
+ R1 –
+
v
– )(210
5
)5()101010(
10
)(
:divider voltage Using
33
3
33
33
26
33
323121
32
VR
R
VRR
R
vRRRRRR
RRv s
NB: notice how R3 controls v
Discussion #5 – Ohm’s LawECEN 301 29
Parallel Resistors Example3: find v
vs = 5V, R1 = 1kΩ, R2 = 1kΩ
V
V
VR
Rv
kR
3
5
)(10210
105
)(210
5
:1 If
33
3
33
3
3
isR2 || R3
vs+_
+ R1 –
+
v
–
NB: notice how R3 controls v
)(12
5
)(102.010
105.0
)(210
5
:1.0 If
33
3
33
3
3
V
V
VR
Rv
kR
Discussion #5 – Ohm’s LawECEN 301 30
Parallel Resistors Example3: find v
vs = 5V, R1 = 1kΩ, R2 = 1kΩ
0v
:0 As 3
R
NB: notice how R3 controls v
2
3
v
:wordsother In 2
5v
: As
v
R
is
+R2
–
vs+_
+R3
–
+ R1 –
+
v
–
Discussion #5 – Ohm’s LawECEN 301 31
Parallel Resistors Example3: find v
vs = 5V, R1 = 1kΩ, R2 = 1kΩ
2
3
Rgh througoes
current no ords,other wIn
0v
:0 As
R
is
+R2
–
vs+_
+ R1 –
+
v
–
Discussion #5 – Ohm’s LawECEN 301 32
Parallel Resistors Example3: find v
vs = 5V, R1 = 1kΩ, R2 = 1kΩ
)R through goesent curr (no
v
:wordsother In 2
5v
: As
3
2
3
v
R
is
+R2
–
vs+_
+ R1 –
+
v
–