To determine Series Vs Parallel Circuits

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To determine whether resistors are in series or parallel, recognize that series connections occur when two elements share a single connection point with no other connections, meaning all current flows through both. In contrast, parallel connections involve elements connected to the same two nodes, resulting in identical voltage drops across them. Complex circuits may contain configurations that are neither purely series nor parallel, making analysis challenging. Redrawing complicated circuits can help clarify the relationships between components. Understanding these principles is essential for analyzing circuit connections effectively.
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Homework Statement


Can any1 teach me how to determine whether something(say resistor) is in series or parallel connection to each other,especially for those complex circuits?
Sometime the circuits given can be very very complex or weird that i couldn't figure out the answers!
Is there some ways or laws for this??
Any respond will be much appreciated!:smile:


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The Attempt at a Solution

 
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When two elements are connected in series, they're connected at one point and nothing else is connected to that point. That means all the current going through one element has to go through the other element as well.

When elements are connected in parallel, they are connected to the same two nodes in the circuit. This means that the voltage drop across the elements are all the same.

One thing to keep in mind is circuit elements can be connected in a way so that they are neither in series nor in parallel. Also, it's often a good idea to redraw complicated circuits so that it becomes clearer what the relationship of the elements are.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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