# Getting Equivalent Resistance WIth delta and star transforms [closed]

I'm trying to solve a circuit using the delta star transformation. Im not being able to get the right answer to the problem which is 10 K Ohms. What is the best way to simplify this circuit? ## closed as off-topic by Voltage Spike, PeterJ, Dave Tweed♦Sep 30 '17 at 13:58

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• You don't need delta-wye transformations to solve that circuit: use symmetry, and you'll get the answer in a minute. – Massimo Ortolano Mar 11 '17 at 18:47
• How do I apply symmetry? Is there anywhere I can read about that? – Pablo Estrada Mar 11 '17 at 18:49
• I'm voting to close this question as off-topic because homework without an attempt at a solution is off-topic – Voltage Spike Sep 30 '17 at 6:08

You don't need $\Delta-Y$ transformations to solve that circuit. Consider the topmost triangle, and divide its base in a series of two $4.5\,\mathrm{k\Omega}$ resistors. You obtain the following circuit (I rearranged the elements with respect to the original circuit): simulate this circuit – Schematic created using CircuitLab

The above circuit is symmetric with respect to the axis crossing the nodes c,d and e: all the resistances on the left are equal to those on the right. This implies that nodes c,d and e are at the same potential: you can short them together without altering the currents flowing in the circuit branches. The simplified circuit is the following: simulate this circuit

You can see that now the network is composed only of series and parallel connections, and since it's symmetric, you can calculate the resistance of just one side and multiply it by two.

You can see that $R_1$, $R_3$ and $R_7$ are in parallel, for an equivalent resistance of $2.25\,\mathrm{k\Omega}$. The total resistance is thus

$$R_\mathrm{ab} = 2\times\frac{(2.25\,\mathrm{k\Omega}+9\,\mathrm{k\Omega})\times 9\,\mathrm{k\Omega}}{2.25\,\mathrm{k\Omega}+9\,\mathrm{k\Omega}+ 9\,\mathrm{k\Omega}} = 10\,\mathrm{k\Omega}$$.

Listen.

1. 9 and 3 on top parallel will yield 6 simulate this circuit – Schematic created using CircuitLab

1. the twin 9 ohm delta from to side will become 3 ohm wye form simulate this circuit

1. 3 & 6 & 3 are in series so just add them simulate this circuit

1. 12 and twin 3 on the bottom are in parallel simulate this circuit