How to find the total resistance of the following circuit

circuit analysisresistors

I tried finding the total resistance but my answer isn't correct. The answer is supposed to be 6.66 kΩ.

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Best Answer

In this case whenever you are calculating the circuit resistance you want the total resistance seen by your only voltage source (18 V battery)

you better start from the node C, Such that i can see a 1 KΩ series with another 1 KΩ enter image description here

The equivalent resistance of this combination is a 2 KΩ resistance so your circuit now looks like this

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i can see now a 2.2 KΩ (Node B) parallel to a 2 KΩ (Node C) enter code here

We can now simply estimate the equivalent resistance of this combination which should be equals to

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Now we place this resistance at node (B) and remove the node (C) branch (Open circuit) or vice verse

Such that your new circuit will look like this

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Now i can see a 22/21 KΩ Series with a 1 KΩ resistance

Such that they are combined into a new resistance of value 43/21 KΩ

Your circuit will look something like this

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Now this circuit can be easily solved you have a 43/21 KΩ parallel with a 2.2 KΩ
and this whole combination equivalent resistance is series with the 5.6 KΩ resistance

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