Circuit Question - Combining/Redrawing Circuits

[Miike012]

Circuit Question -- Combining/Redrawing Circuits

I don't understand how they the circuit on the left was redrawn to be the circuit on the right.

1. How did they know R₁ and E₁ were parallel to R₂ and E₂ and the 6 ohm resistor?

2. How did they know that E₁ should be position as it is in the picture? Same question for E₂.

 

[phinds]

You think you could make the image just a little smaller? I can almost read this one.

 

[Miike012]

You think you could make the image just a little smaller? I can almost read this one.

I hope this one is better

 

[collinsmark]

I don't understand how they the circuit on the left was redrawn to be the circuit on the right.

1. How did they know R₁ and E₁ were parallel to R₂ and E₂ and the 6 ohm resistor?

2. How did they know that E₁ should be position as it is in the picture? Same question for E₂.

Take the nodes marked E₁ and E₂ in the first picture, and place ideal, constant voltage sources (or ideal batteries in this case) with the appropriate emf (voltage) between those nodes and ground. Connect all your grounds, and you should get the second picture (except without R_L, since that wasn't in the blue part).

For example, in the first picture, E₁ is just hanging there at -6 V. Instead of letting it hang there like that, add in a 6 V source between E₁ and ground, paying attention to the polarity such that the original point E₁ is negative 6 V with respect to ground. Do the same sort of thing for E₂ (except +10 V). Then connect all the grounds together.

You can do that because when a node is "hanging" at a constant voltage like that, it is assumed that a voltage source is present, even though it's not in the diagram. So it's okay to put one in. You're not violating anything with lumped-parameter circuit theory by doing so.

 

[HalfLostAndSearching]

3. How did they know the 6 ohm resistor should be positioned as it is in the picture?

I would approach this question by first understanding the fundamental principles of circuit analysis. In this case, it appears that the circuit was redrawn using the rules of parallel and series resistors. When resistors are connected in parallel, the total resistance is equal to the reciprocal of the sum of the reciprocals of each individual resistance. Similarly, when resistors are connected in series, the total resistance is equal to the sum of the individual resistances.

Based on this understanding, it seems that in the redrawn circuit, R1 and E1 are in parallel with R2 and E2, since they share the same endpoints. This means that the total resistance of that branch is equal to the reciprocal of the sum of the reciprocals of R1 and E1, which is then in series with the 6 ohm resistor.

As for the positioning of E1 and E2, it is likely that they were placed in that position to maintain the same voltage drop across each resistor in the circuit. This is because in parallel circuits, the voltage drop across each individual resistor is the same, while in series circuits, the voltage drop is divided among the resistors.

The positioning of the 6 ohm resistor could also be determined using the rules of series and parallel resistors. In this case, it appears that the 6 ohm resistor is in series with the branch containing R1 and E1, and is also in parallel with the branch containing R2 and E2.

Overall, it seems that the redrawn circuit was created by applying the principles of parallel and series resistors, along with maintaining the same voltage drop across each resistor. These are fundamental concepts in circuit analysis and can be used to simplify complex circuits and make them easier to understand and analyze.