Travis Cannon
- Mar 24, 2014
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I'd start by drawing out a circuit for each of the given bulb combinations, leaving out the switches. Note that some bulbs need to be in series and some in parallel to get the indicated voltages.
Then compare the resulting circuits and see where you would insert the switches to achieve the specified combinations by closing the switches.
Then compare the resulting circuits and see where you would insert the switches to achieve the specified combinations by closing the switches.
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Travis Cannon
- Mar 24, 2014
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What really gets me, is how all the switches can be closed but still have one of the lights off, how is that possible?
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Travis,
I moved this threaad to the homework section.
Before we start guiding you along, show us what you have donw so far to tackel the problem yourself and where you have failed.
Tip: You can deal with the lamps as ordinary resistors (you do not have to know their value!) each lamp has the same resistance (not completely realistic but good enough for this homework). Resistors can be connected in series and in parallel, lamps too, dividing the battery voltage in various ways depending on the connections.
Connections can be opened and closed by the switches.
I moved this threaad to the homework section.
Before we start guiding you along, show us what you have donw so far to tackel the problem yourself and where you have failed.
Tip: You can deal with the lamps as ordinary resistors (you do not have to know their value!) each lamp has the same resistance (not completely realistic but good enough for this homework). Resistors can be connected in series and in parallel, lamps too, dividing the battery voltage in various ways depending on the connections.
Connections can be opened and closed by the switches.
There's two ways to stop current flowing through a bulb. One way is by breaking the circuit to the bulb. The other way is... ??? hint #1: 5 letters starting with "S".... hint #2, no current flows through the bulb but current still flows somewhere.
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Travis,
please: 1 topic, 1 thread.
I merged your two threads into this one so everyone can follow the discussion.
please: 1 topic, 1 thread.
I merged your two threads into this one so everyone can follow the discussion.
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A switch can be connected in series to a lamp or in parallel ...
Travis Cannon
- Mar 24, 2014
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What does it mean that all voltages shown are approximate? How accurate is approximate?
For instance, take the 'all switches closed' configuration. It would seem that there would be two lamps in series with two lamps in parallel. But that would mean that the two lamps in series would each have an individual resistance much greater than the individual resistance of the lamps in parallel, and the difference is too great to be labeled 'approximate'. But in the real world the resistance of a lamp filament varies with the brightness of the lamp. A cold filament has much lower resistance than a hot filament.
If the temperature effect is taken into account, then the given voltages make make much more sense.
For instance, take the 'all switches closed' configuration. It would seem that there would be two lamps in series with two lamps in parallel. But that would mean that the two lamps in series would each have an individual resistance much greater than the individual resistance of the lamps in parallel, and the difference is too great to be labeled 'approximate'. But in the real world the resistance of a lamp filament varies with the brightness of the lamp. A cold filament has much lower resistance than a hot filament.
If the temperature effect is taken into account, then the given voltages make make much more sense.
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I think it means "assume the lamps have a constant and equal resistance"
Assumption of equality will certainly lead one to the same circuit configurations (because what else is there?), but it irks me that calculated values are so far from the given values yet still deemed close enough, 'approximate'. Makes me wonder whether the given voltages were calculated, or measured from a working model of the device.
Since the switch/lamp-voltage table looks a lot like a truth table, what design hints could a Karnaugh mapping provide?
The first thing that stands out is that L1 and L5 are identical. This can only happen if they are in series or in parallel. But parallel won't drop enough voltage so they must be in series and connected as a single bulb.
Now look for groups of four. L2 is always off when S1 is open. So L2 must be in series with S1. Both L3 and L4 are always off when S2 is open. So S2 must be in series with L3 and L4.
L4 is always off when S3 is closed. So S3 must be in parallel with L4.
The voltage drops give the series/parallel configuration of the lamps, while the K-map gives the configuration of the switches. It's not a complete design but it should be enough to get to the point where the solution is obvious.
The first thing that stands out is that L1 and L5 are identical. This can only happen if they are in series or in parallel. But parallel won't drop enough voltage so they must be in series and connected as a single bulb.
Now look for groups of four. L2 is always off when S1 is open. So L2 must be in series with S1. Both L3 and L4 are always off when S2 is open. So S2 must be in series with L3 and L4.
L4 is always off when S3 is closed. So S3 must be in parallel with L4.
The voltage drops give the series/parallel configuration of the lamps, while the K-map gives the configuration of the switches. It's not a complete design but it should be enough to get to the point where the solution is obvious.
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