I have the answer to the following problem, but I am not sure how they got it. Please explain:

Four identical incandescent light bulbs L1, L2, L3, L4, and a battery are connected as shown on the diagram on the right. The three switches S1, S2, S3 are open. How will the brightness of the four lamps change compared to the original state if the specified switches are closed (all other switches are open)?

Example: S1 closed.
Expected Answer: L1 - off, L2 - same, L3 - brighter, L4 - brighter.

Answer the following scenario:
(A) S2 closed;
(B) S3 closed;
(C) S1 and S2 closed;
(D) S2 and S3 closed.

The given answer:

A) Answer: L1 - brighter, L2 - same, L3 - off, L4 - off
B) Answer: L1 - off, L2 - same, L3 - off, L4 - brighter
C) Answer: all lamps off (short circuit)
D) Answer: L1 - brighter, L2 - same, L3 - brighter

Thank you so much!

the circuit

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    \$\begingroup\$ I recommend grounding the lower-left corner wire and then redrawing the schematic so that it is not so confusing. As you work to unwind it, I believel things will become much much clearer to you and you won't even need us to help out. (In fact, it's what I'd have to do myself before bothering to consider an answer.) \$\endgroup\$ – jonk Apr 4 at 21:44
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    \$\begingroup\$ We don't hand out answers to homework here without seeing the OP demonstrate that they have done a substantial amount of work. Show us all of your work and then ask a specific question. I know you think you have "the answer" but in many cases the "how" is the real answer you are expected to provide. \$\endgroup\$ – Elliot Alderson Apr 4 at 21:45
  • \$\begingroup\$ GoldenRetriever - Hi, I see that you removed the "homework" tag that I added. I have reinstated that. This is a homework-type question, and it will be treated that way here. In other words, please edit the question and add your own attempt at explaining the behaviours for scenarios (A) - (D). Show where you get stuck in your analysis. Then readers can explain more. Failure to add your own solution attempt is likely to cause the question to be closed (actually, put on-hold) quickly. Thank you. \$\endgroup\$ – SamGibson Apr 4 at 23:11
  • \$\begingroup\$ I have the answer to the following problem ... there are four solutions, not one ... which one do you not understand \$\endgroup\$ – jsotola Apr 5 at 2:07

Here's how I'd redraw your schematic:


simulate this circuit – Schematic created using CircuitLab

I think you should be quite able to work out the details for yourself from the above. It's now "easy to read." You really should exercise your skills in redrawing schematics. It will take you very, very far in situations like this one.

For example, it is now very easy to see that closing both \$SW_1\$ and \$SW_2\$ will short out the power supply. You can also easily see that no switches affect \$LAMP_2\$ unless they short out the power supply.

So please, please, please learn to redraw schematics you are given.

See below:

Redrawing Schematic Addendum

Rules to live by are:

  • Arrange the schematic so that conventional current appears to flow from the top towards the bottom of the schematic sheet. I like to imagine this as a kind of curtain (if you prefer a more static concept) or waterfall (if you prefer a more dynamic concept) of charges moving from the top edge down to the bottom edge. This is a kind of flow of energy that doesn't do any useful work by itself, but provides the environment for useful work to get done.
  • Arrange the schematic so that signals of interest flow from the left side of the schematic to the right side. Inputs will then generally be on the left, outputs generally will be on the right.
  • Do not "bus" power around. In short, if a lead of a component goes to ground or some other voltage rail, do not use a wire to connect it to other component leads that also go to the same rail/ground. Instead, simply show a node name like "Vcc" and stop. Busing power around on a schematic is almost guaranteed to make the schematic less understandable, not more. (There are times when professionals need to communicate something unique about a voltage rail bus to other professionals. So there are exceptions at times to this rule. But when trying to understand a confusing schematic, the situation isn't that one and such an argument "by professionals, to professionals" still fails here. So just don't do it.) This one takes a moment to grasp fully. There is a strong tendency to want to show all of the wires that are involved in soldering up a circuit. Resist that tendency. The idea here is that wires needed to make a circuit can be distracting. And while they may be needed to make the circuit work, they do NOT help you understand the circuit. In fact, they do the exact opposite. So remove such wires and just show connections to the rails and stop.
  • Try to organize the schematic around cohesion. It is almost always possible to "tease apart" a schematic so that there are knots of components that are tightly connected, each to another, separated then by only a few wires going to other knots. If you can find these, emphasize them by isolating the knots and focusing on drawing each one in some meaningful way, first. Don't even think about the whole schematic. Just focus on getting each cohesive section "looking right" by itself. Then add in the spare wiring or few components separating these "natural divisions" in the schematic. This will often tend to almost magically find distinct functions that are easier to understand, which then "communicate" with each other via relatively easier to understand connections between them.
  • You get to choose exactly one node and call it "ground." If the purpose of redrawing the schematic is for understanding it, then choose a node that helps achieve that. When signals are single-ended, they share a common node and you should select this common node as "ground." If the purpose is for analysis, then you can select this for the purpose of reducing the equation complexity. Often, this will mean the node that is "busiest" (has the most terminals attached to it.) Either way, make this choice wisely and it will help a great deal.

The above rules aren't hard and fast. But if you struggle to follow them, you'll find that it does help a lot.

You can read a snippet of my own education by those schematic draftsmen at Tektronix who trained me by reading here.


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