COMPARING SERIES/PARALLEL CIRCUITS

KEY
CombinationsHow many ways when counting just once for all orders of given items   COMBProvides all theoretically possible combinations.
PermutationsHow many ways when counting all the different orders of items   PERMProvides all theoretically possible permutations.
ONCOProvides all theoretically possible combinations except OFF.   ONPEProvides all theoretically possible permutations except OFF.
YESProvides the feature.   noDoes not provide the feature, or can't provide all possible combinations.
noneDoesn't provide any of the theoretically possible combinations.   -No theoretically possible combinations exist.
Polarity SafeAlways gives each load the proper polarity.   Neutral SafeNever allows a hot connection without a neutral connection.
THEORETICAL MAXIMUM OF POSSIBLE WAYS
Number
of Loads
n		 Number of Combinations Number of Permutations
Series Off and
Parallel		 Series-
Parallel		 Parallel
-Series		 Other
Combo		 Total Series Off and
Parallel		 Series-
Parallel		 Parallel
-Series		 Other
Combo		 Total
2 140005 240006
3 4833018 12866032
4 1116252524101 6016746672288
INDIVIDUALIZED DESIGNS
Series/
Parallel
System
Name		  
Number
of
Lamps
n		 Number of
Switches		 Number of
Permutations		 Has All Combinations
or Permutations		 Has All
Positions
Polarity
Safe		 Has All
Positions
Neutral
Safe
All
Switches		Multi
Pole		 Throw
> 2		 Switch
Pos.		Useful
Pos.		 Photog.
Pos.		 SeriesParallel Series-
Parallel		Parallel
-Series		 All
Other
Orig 2-lamp2110 222 COMBno--- YESYES
SEPAR 2012111 333 COMBno--- YESno
SEPAR 2022200 443 COMBno--- nono
SEPAR 2032201 653 COMBPERM--- YESno
SEPAR 2042221 653 COMBPERM--- YESYES
SEPAR 3013301 1275 nonononenone- nono
SEPAR 3023400 16115 nonononone- nono
SEPAR 303*32 (1)1 (2)0 4 (2)4 (2)2 nonononenone- nono
SEPAR 3053400 16105 nonononeno- nono
SEPAR 3063210 444 nonononenone- nono
SEPAR 3073300 875 nonononenone- nono
SEPAR 3103301 1275 nonononenone- nono
SEPAR 3123503 108185 COMBPERMCOMBCOMB- nono
SEPAR 4014704 648477 COMBPERMnonono nono
SEPAR 401A4804 864559 COMBPERMnonono nono
SEPAR 402A4500 32248 nonononenonone nono
SEPAR 40941200 864 **56 ***9 *** COMBPERMnonono nono

* The values in parentheses are obtained when both switches are ganged to operate together.
** If more than one switch per group is allowed to be on (redundant), there are 4096 possible positions.
*** One more position is available to safely change lamps with screw shells connected to neutral.
 
REGULAR SWITCHING MATRIX
Series/
Parallel
System
Name		  
Number
of
Lamps
n		 Number of
Switches		 Number of
Permutations		 Has All Combinations
or Permutations		 Has All
Positions
Polarity
Safe		 Has All
Positions
Neutral
Safe
All
Switches		Multi
Pole		Throw
> 2		 Switch
Pos.		Useful
Pos.		Photog.
Pos.		 SeriesParallelSeries-
Parallel		Parallel
-Series		 All
Other
SEPAR n00Z†nnnn (2n+1)n?2n-1 PERMPERMnoPERMno YESno
SEPAR n00n2n0n (2n+2)n?2n-1 PERMPERMnoPERMno YESno
SEPAR 2002402 3663 PERMPERM--- YESno
SEPAR 3003603 512295 PERMPERMnoPERM- YESno
SEPAR 4004804 10000?7 PERMPERMnoPERMno YESno
SEPAR nn0nn2n2-2nn (2n2-n)(3n)?2n-1 PERMPERMPERMPERMPERM nono
SEPAR 2202402 3663 PERMPERM--- YESno
SEPAR 3303933 1728325 PERMPERMPERMPERM- nono
SEPAR 44041684 3317762887 PERMPERMPERMPERMPERM nono

† This is the original form of SEPAR n00, made when multiple-gang switches were easily bought. Instead of two single-pole switches (one with 2 positions and one with n+1 positions), it has a single switch for each lamp with 2n+1 position. It is functionally identical.
 
INFINITE SWITCHING MATRIX
Series/
Parallel
System
Name		  
Number
of
Lamps
n		 Number of
Switches		 Number of
Permutations		 Has All Combinations
or Permutations		 Has All
Positions
Polarity
Safe		 Has All
Positions
Neutral
Safe
All
Switches		Multi
Pole		Throw
> 2		 Switch
Pos.		Switch
Pos.†††		 Useful ||
Photog.		 SeriesParallelSeries-
Parallel		Parallel
-Series		 All
Other
SEPAR I-nZ ††n2n02n (n+2)2n(n+2)2n ? || 2n-1 PERMPERMPERMPERMPERM nono
SEPAR I-nn2n(n+1)00 (n+2)2n22n(n+1) ? || 2n-1 PERMPERMPERMPERMPERM nono
SEPAR I-221200 2564096 6 ;|| 3 PERMPERM--- nono
SEPAR I-332400 1562516777216 29 || 5 PERMPERMPERMPERM- nono
SEPAR I-444000 1679616240288 || 7 PERMPERMPERMPERMPERM nono
SEPAR I-556000 282475249260? || 7 PERMPERMPERMPERMPERM nono

†† This is the rotary switch form of SEPAR I-n. It is functionally identical.
††† The number of positions if more than one switch per group is allowed to be on (redundant)
 
SP-STD POWER LINE SWITCHING
Series/
Parallel
System
Name		  
Number
of
Lamps
n		 Number of
Switches		 Number of
Permutations		 Has All Combinations
or Permutations		 Has All
Positions
Polarity
Safe		 Has All
Positions
Neutral
Safe
All
Switches		Multi
Pole		Throw
> 2		 Switch
Pos.		Useful
Pos.		Photog.
Pos.		 SeriesParallelSeries-
Parallel		Parallel
-Series		 All
Other
SP-STD 22220 4‡4‡2‡ COMBONPE‡--- YESYES
SP-STD 33440 16‡13‡4‡ COMBONPE‡nono- YESYES
SP-STD 44660 64‡40‡8‡ COMBONPE‡nononone YESYES
SP-STD SETSn2n-22n-20 22n-2‡??‡ COMBONPE‡nonono YESYES
SP-STD SWAP A3660 64‡174 COMBONPE‡COMBCOMB- YESYES
SP-STD SWAP B3770 128‡284 PERMONPE‡COMBCOMB- YESYES
SP-STD SWAP C4880 256‡?6 COMBONPE‡nonono YESYES

‡ The SP-STD series does not provide an OFF position. A separate switch that turns off the entire setup can be added.

See the STD SWAP circuits here.
 

Analysis shows that it is impossible to make a polarity-safe and neutral-safe circuit that allows all possible series/parallel combinations (let alone permutations).
This is because possible circuits include bridge circuits where the polarities of some loads are determined by the impedances of other loads.
 

The SP-STD Cord and Plug Modules can not make the combinations that produce bridge circuits, so they are polarity-safe and neutral-safe.
 
BATTERY SWITCHING, GUITAR SWITCHING, AND SPEAKER SWITCHING
These are specialized circuits. Since the goals of these circuits are not to provide the greatest number of different series-parallel combinations, this kind of chart is rather useless for such circuits. Therefore, they are not shown here.
 

LINKS:

  1. SELECTING SERIES OR PARALLEL OPERATION (Main Page)
  2. LIGHT BULBS, SPECTRA, and HUMAN VISION
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