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.