Finding equivalent resistance of a resistor network

Question

In the circuit below, all of the resistors are 15 Ohms. I am trying to find the equivalent resistance between A and B.

Can we argue that since R_AD/R_DC = R_AO/R_OC that AODC is a wheatstone bridge and thus say no current will flow through DO and remove DO from the circuit? Using the same argument, can we remove BO too?

Can we then just simplify the circuit like below and then find the equivalent resistance using the series and parallel rules?

Answer 1

I’d suggest you consider the schematic below:

^{simulate this circuit – Schematic created using CircuitLab}

What is the voltage between O1 and O2? What current would flow through a resistor you would add between those nodes? What if you replace that resistor with a wire?

Answer 2

Equivalent Resistor is 8 Ohm.

Equivalent resistor is independent of voltage applied at Node A and Node B, so, for simplicity assume that Node A is at 1V and Node B is at 0V. Split current and use kirchoff rule at 3 nodes.

Answer 3

This problem can be solved fairly easily using Delta to Star Transformations. Recognizing the left and right delta and converting each resistor yields an equivalent resistance of 5R in each leg of the star. After that it is a simple matter of combining series and parallel resistors.

^{simulate this circuit – Schematic created using CircuitLab}

Answer 4

By looking at the circuit due to lack of symmetry, it can be said that D,O,B are not at same potential, so what you have done is incorrect if equivalent resistance is to be found across AB.

But the second inage is correct if you are finding resistance across AC. The first answer gives some insight why it should be correct for this case.