Series/Parallel Resistor Reduction

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SERIES PARALLEL RESISTOR COMBINATIONS
UP TO NOW WE HAVE STUDIED CIRCUITS THAT CAN BE
ANALYZED WITH ONE APPLICATION OF KVL(SINGLE LOOP)
OR KCL(SINGLE NODE-PAIR)
WE HAVE ALSO SEEN THAT IN SOME SITUATIONS IT IS
ADVANTAGEOUS TO COMBINE RESISTORS TO SIMPLIFY
THE ANALYSIS OF A CIRCUIT
NOW WE EXAMINE SOME MORE COMPLEX CIRCUITS WHERE
WE CAN SIMPLIFY THE ANALYSIS USING THE TECHNIQUE
OF COMBINING RESISTORS PLUS THE USE OF OHMS
LAW
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6k3k
(10K,2K)SERIES
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(No Transcript)
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EXAMPLES COMBINATION SERIES-PARALLEL
If the drawing gets confusing Redraw the reduced
circuit and start again
RESISTORS ARE IN SERIES IF THEY CARRY EXACTLY THE
SAME CURRENT
RESISTORS ARE IN PARALLEL IF THEY ARE CONNECTED
EXACTLY BETWEEN THE SAME TWO NODES
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AN INVERSE SERIES PARALLEL COMBINATION
Given the final value Find a proper combination
SIMPLE CASE
NOT SO SIMPLE CASE
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EFFECT OF RESISTOR TOLERANCE
RANGES FOR CURRENT AND POWER?
THE RANGES FOR CURRENT AND POWER ARE DETERMINED
BY THE TOLERANCE BUT THE PERCENTAGE OF CHANGE
MAY BE DIFFERENT FROM THE PERCENTAGE OF
TOLERANCE. THE RANGES MAY NOT EVEN BE SYMMETRIC
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CIRCUIT WITH SERIES-PARALLEL RESISTOR COMBINATIONS
THE COMBINATION OF COMPONENTS CAN REDUCE THE
COMPLEXITY OF A CIRCUIT AND RENDER IT SUITABLE
FOR ANALYSIS USING THE BASIC TOOLS DEVELOPED SO
FAR.
COMBINING RESISTORS IN SERIES ELIMINATES ONE NODE
FROM THE CIRCUIT. COMBINING RESISTORS IN PARALLEL
ELIMINATES ONE LOOP FROM THE CIRCUIT

• GENERAL STRATEGY
• REDUCE COMPLEXITY UNTIL THE CIRCUIT
• BECOMES SIMPLE ENOUGH TO ANALYZE.
• USE DATA FROM SIMPLIFIED CIRCUIT TO
• COMPUTE DESIRED VARIABLES IN ORIGINAL
• CIRCUIT - HENCE ONE MUST KEEP TRACK
• OF ANY RELATIONSHIP BETWEEN VARIABLES

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FIRST REDUCE IT TO A SINGLE LOOP CIRCUIT
SECOND BACKTRACK USING KVL, KCL OHMS
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LEARNING BY DOING
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AN EXAMPLE OF BACKTRACKING
A STRATEGY. ALWAYS ASK WHAT ELSE CAN I COMPUTE?
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THIS IS AN INVERSE PROBLEM WHAT CAN BE COMPUTED?
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THIS CIRCUIT HAS NO RESISTOR IN SERIES OR
PARALLEL
Ra(RcR4)(RbR5)
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REPLACE IN THE THIRD AND SOLVE FOR R1
SUBTRACT THE FIRST TWO THEN ADD TO THE THIRD TO
GET Ra
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LEARNING EXAMPLE APPLICATION OF WYE-DELTA
TRANSFORMATION
ONE COULD ALSO USE A WYE - DELTA TRANSFORMATION
...
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LEARNING EXAMPLE
THE RESULTING CIRCUIT IS A CURRENT DIVIDER
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CIRCUIT AFTER PARALLEL RESISTOR REDUCTION
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LOW
HIGH
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WHEN THE STARTER IS ENGAGED THE VOLTAGE DROP
ACROSS THE RESISTENCE INCREASES 100 FOLD ---
LIGHTS DIM!
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Measure R3 with scale empty Measure R3 when truck
is on sclae
Weight is determined in the following manner.
The change in R3 required to balance the bridge
represents the change in strain, which when
multiplied by the modulus of elasticity yields
the change in stress. The change in stress
multiplied by the cross-sectional area of the
cylinder produces the change in load, which
determines the weight
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Lowest V2 All lamps ON (5 lamps in parallel with
R2)
Equivalent circuit
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Design a current-to-voltage converter that will
output 5 V when the current signal Is 20mA
Assume that the controller does not use any
current from the I to V converter. In this case a
simple resistor behaves as current to voltage
converter!
Wire resistance does not matter! (within
reasonable limits)