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I have a certain circuit only containing resistors of different values. There is one 'input' and one 'output' for the current. How do I calculate the equivalent resistance of the circuit? Are there any basic rules to follow?

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If determining replacement value is the only goal then I can think of the following steps:

1) Analyse the circuit into the smallest solvable sub-circuits possible (series and parallel);

2) Calculate series resistors \$R_S = R_1 + R_2\$;

schematic

simulate this circuit – Schematic created using CircuitLab

3) Calculate parallel resistors: \$R_P = \frac{1}{\frac{1}{R_3}+\frac{1}{R_4}}\$

schematic

simulate this circuit

4) Apply wye-delta (Y-Δ) transform or reverse

5) Repeat until solved or run the circuit through a circuit simulator like SPICE.

Wye-delta (Y-Δ) transform

schematic

simulate this circuit

Y→Δ

$$R_{ab} = R_{an} + R_{bn} + \frac{ R_{an} \cdot R_{bn} }{ R_{cn} }$$

$$R_{ac} = R_{an} + R_{cn} + \frac{ R_{an} \cdot R_{cn} }{ R_{an} }$$

$$R_{bc} = R_{bn} + R_{cn} + \frac{ R_{bn} \cdot R_{cn} }{ R_{an} }$$

Δ→Y

$$R_{an} = \frac{ R_{ab} \cdot R_{ac} }{ R_{ab} + R_{ac} + R_{bc} }$$

$$R_{bn} = \frac{ R_{ab} \cdot R_{bc} }{ R_{ab} + R_{ac} + R_{bc} }$$

$$R_{cn} = \frac{ R_{ac} \cdot R_{bc} }{ R_{ab} + R_{ac} + R_{bc} }$$

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  • \$\begingroup\$ This is a good answer, straight to the point. Perhaps clarifying with examples and an explanation of wye-delta would make it even better? :-) (I meant this to be easily understandable for beginners, and think they will yike seeing that wiki :-)) \$\endgroup\$ – user17592 Mar 14 '13 at 19:51
  • \$\begingroup\$ Ooh, cool. Wish I could upvote you some more for that edit! \$\endgroup\$ – user17592 Mar 14 '13 at 20:54
  • \$\begingroup\$ In Dutch it is called "ster-driehoek transformatie" (star-triangle transform). \$\endgroup\$ – jippie Mar 14 '13 at 22:15
  • \$\begingroup\$ driehoek always makes me smile. Three-Corner! \$\endgroup\$ – stanri Mar 15 '13 at 0:41
  • \$\begingroup\$ @StaceyAnne Oh, it's a horror, really. For every mathematical term we have a different one. Fault of this guy. Driehoek isn't that bad, triangular is basically three-corner as well. But why do we have to call mathematics wiskunde (science of that what's true)!? \$\endgroup\$ – user17592 Mar 15 '13 at 8:05

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