Series/Parallel Resistor Reduction
RESISTIVE CIRCUITS
? SERIES/PARALLEL RESISTOR COMBINATIONS - A TECHNIQUE
TO REDUCE THE COMPLEXITY OF SOME CIRCUITS
? LEARN TO ANALYZE THE SIMPLEST CIRCUITS
? THE VOLTAGE DIVIDER
? THE CURRENT DIVIDER
? WYE - DELTA TRANSFORMATION - A TECHNIQUE TO REDUCE
COMMON RESISTOR CONNECTIONS THAT ARE NEITHER SERIES NOR
PARALLEL
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 OHM¡¯S LAW
SERIES COMBINATIONS
PARALLEL COMBINATION
G p = G1 + G2 + ... + G N
FIRST WE PRACTICE COMBINING RESISTORS
3k
SERIES
6k||3k
(10K,2K)SERIES
6k || 12k = 4k
5k¦¸
3k
12k
EXAMPLES COMBINATION SERIES-PARALLEL
9k
If the drawing gets confusing¡
Redraw the reduced circuit
and start again
18k || 9k = 6k
RESISTORS ARE IN SERIES IF THEY CARRY
EXACTLY THE SAME CURRENT
6k + 6k + 10k
RESISTORS ARE IN PARALLEL IF THEY ARE
CONNECTED EXACTLY BETWEEN THE SAME TWO
NODES
EFFECT OF RESISTOR TOLERANCE
NOMINAL RESISTOR VALUE : 2.7k¦¸
RESISTOR TOLERANCE : 10%
RANGES FOR CURRENT AND POWER?
?
10
NOMINAL CURRENT : I =
= 3.704 mA
2.7
(10)
2.7
_
= 37.04 mW
10
= 3.367 mA
MINIMUM POWER(VImin ) : 33.67 mW
1.1¡Á 2.7
10
=
= 4.115 mA MAXIMUM POWER : 41.15 mW
0.9 ¡Á 2.7
MINIMUM CURRENT : I min =
MAXIMUM CURRENT : I max
NOMINAL POWER : P =
2
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