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Series and Parallel Resistors. Objective of Lecture. Explain mathematically how resistors in series are combined and their equivalent resistance. Chapter 2.5 Explain mathematically how resistors in parallel are combined and their equivalent resistance. Chapter 2.6 - PowerPoint PPT Presentation
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Objective of LectureExplain mathematically how resistors in
series are combined and their equivalent resistance.Chapter 2.5
Explain mathematically how resistors in parallel are combined and their equivalent resistance.Chapter 2.6
Rewrite the equations for conductances.
Series Resistors
Series Resistors (con’t)Use KVL
210 VVVin
Series Resistors (con’t)Use KVL
Use Ohm’s Law
22
11
IRV
IRV
210 VVVin
Series Resistors (con’t)Use KVL
Use Ohm’s Law
Substitute into KVL equation
)(
0
2121
21
RRIIRIRV
IRIRV
in
in
22
11
IRV
IRV
210 VVVin
Equivalent Resistance: Series Connections
Req is equal to the sum of the resistors in series.
In this case: Req = R1 + R2
General Equations: Series ResistorsIf S resistors are in series, then
where Vin may be the applied
voltage or the total voltage dropped across all of the resistors in series.
S
sseq
S
ssin
RR
RIV
1
1
Parallel Resistors
Parallel Resistor (con’t)Use KCL
210 III in
Parallel Resistor (con’t)Use KCL
Use Ohm’s Law210 III in
22
11
RIV
RIV
R
R
Parallel Resistor (con’t)Use KCL
Use Ohm’s Law
Substitute into KCL equation
210 III in
22
11
RIV
RIV
R
R
2121
21
21
/
11
0
RRRRVI
RRVI
RVRVI
Rin
Rin
RRin
Equivalent Resistance: Parallel Connections
1/Req is equal to the sum of the inverse of each of the resistors in parallel.
In this case:
1/Req = 1/R1 + 1/R2
Simplifying (only for 2 resistors in parallel)
Req = R1R2 /(R1 + R2)
General Equations: Parallel ResistorsIf P resistors are in parallel, then
where Iin may be the total current flowing into and out of the nodes shared by the parallel resistors. 1
1
1
1
P
p peq
P
p p
Rin
RR
R
VI
If you used G instead of RIn series:
The reciprocal of the equivalent conductance is equal to the sum of the reciprocal of each of the conductors in series
In this example
1/Geq = 1/G1 + 1/G2
Simplifying (only for 2 conductors in series)
Geq = G1G2 /(G1 + G2)
If you used G instead of RIn parallel:
The equivalent conductance is equal to the sum of all of the conductors in parallel
In this example:
Geq = G1 + G2
Electronic Response:For the same value resistors
As you increase the number of resistors in series
Does Req increases or decreases?
As you increase the number of resistors in parallel
Does Req increases or decreases?
SummaryThe equivalent resistance and conductance of
resistors in series are:
where S is the total number of resistors in series.
The equivalent resistance and conductance of resistors in parallel are:
where P is the total number of resistors in parallel.
P
ppeq
P
p peq GG
RR
1
-1
1
1
1
11
1
S
s seq
S
sseq G
GRR
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