Electronic – Equivalent resistance of a circuit

resistanceresistors

Circuit in question

This is the solution I saw for the equivalent resistance:
"12 and 60 ohm resistors are in parallel. Hence, 12//60 = 10 ohm. This 10 ohm
and 20 ohm are in series to give 30 ohm. This is in parallel with 30 ohm to give
30//30 = 15 ohm. And 25//(15+10) = 12.5. Thus R = 5 + 12.5 + 15 = 32.5 ohm"

I would really appreciate a circuit diagram solution, one that shows the circuit after each step so that I can properly understand the solution.

schematic

simulate this circuit – Schematic created using CircuitLab

Figure 2. CircuitLab version for OP to work on [by Transistor].

Best Answer

I know that Michael took a numerical solution approach, using tools. But sometimes an ape doesn't have their tools with them and have only their fingers with which to draw in the sand and a brain to apply.

In such a situation you might consider the following initial steps:

schematic

simulate this circuit – Schematic created using CircuitLab

Now, from your own post above:

12 and 60 ohm resistors are in parallel. Hence, 12//60 = 10 ohm. This 10 ohm and 20 ohm are in series to give 30 ohm. This is in parallel with 30 ohm to give 30//30 = 15 ohm. And 25//(15+10) = 12.5. Thus R = 5 + 12.5 + 15 = 32.5 ohm

You should be now able to see why the highlighted line above might be a first step towards a solution.

Note that the use of a convenient, temporary ground doesn't violate anything. All it does is help a little in "seeing" how you might combine things. Sometimes, lots of wires get in the way of being able to see better. If so, just cut them away and name the end-point, instead. Getting rid of wires can really help, at times. (You can always re-connect them back up and un-name them, later.)

At this point, it should be easy to see how the next step you quoted might occur. Remember?

12 and 60 ohm resistors are in parallel. Hence, 12//60 = 10 ohm. This 10 ohm and 20 ohm are in series to give 30 ohm. This is in parallel with 30 ohm to give 30//30 = 15 ohm. And 25//(15+10) = 12.5. Thus R = 5 + 12.5 + 15 = 32.5 ohm

Can you now see how that happens, looking at the schematic in the lower right corner?

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