Ignoring nodes/wires when combining resistors to find equivalent resistance

Question

Is the 2nd step in the solution sheet wrong?

I don't know how they can just ignore the node where the 9 ohm resistor and the 12 ohm resistor were located. Wouldn't current be branched/divided when it flows from either the a or the b terminal through both the 18 and 9 ohm; and 12 and 6 ohm resistors, thus making the 2nd picture not a series circuit?

Answer 1

Look harder at the schematic and you will see this: -

• The 9 ohm and 18 ohm are in parallel
• The 6 ohm and 12 ohm are in parallel

Just keep looking is my advice and follow the red enclosed node around from top to bottom.

It's a teaching aid to make you realize how things are connected together.

Answer 2

Re-arranging circuit components in an effort to aid circuit simplification is a skill that engineers use so very often that we often do it mentally. Re-arranging can make clear that nodes are common (as in this case), or that components are in parallel or in series. This re-arranging skill is particularly useful when applying Thevenin or Norton equivalents.

^{simulate this circuit – Schematic created using CircuitLab}

Satisfy yourself that a test current applied from Node A -to- Node B would measure the same in the red-coloured wires in any of the diagrams shown.