I have started learning circuit analysis and when I came across finding equivalent resistances of complex circuits, I found that complex circuits can be redrawn to simpler circuits. However, I am not able to understand how we can redraw the circuit. What are the rules for redrawing a circuit?

  • $\begingroup$ Have you tried googling your title? $\endgroup$ Aug 22 '16 at 13:59
  • $\begingroup$ Yes, but i really am not able to completely understand it. $\endgroup$
    – Tejesh Atr
    Aug 22 '16 at 14:01
  • $\begingroup$ Not able to understand what exactly? $\endgroup$ Aug 22 '16 at 14:01
  • $\begingroup$ How can we decide that two circuits are ACTUALLY equivalent? The websites where i saw about this topic mentioned two or more junctions and spread them out but few connections dont seem obvious $\endgroup$
    – Tejesh Atr
    Aug 22 '16 at 14:03
  • $\begingroup$ Spread them out such that the complex circuit becomes a simple linear circuit $\endgroup$
    – Tejesh Atr
    Aug 22 '16 at 14:05

The purpose of redrawing a circuit is to help you to see more clearly what the connections are. In particular, you want to see if it is possible to simplify the circuit - eg by replacing series or parallel combinations of resistors by a single equivalent resistance - before using the circuit for calculation or simulation.

Redrawing and simplifying a circuit is not necessary if it is already clear to you. You can apply Kirchhoff's Rules methodically without doing either. However, making the connections more obvious and reducing the number of circuit elements will enable you to solve the circuit with less effort and reduce the chances of making a mistake.

There is no standard method for redrawing. The key requirement is that all the connections must be kept exactly the same. In mathematical terminology, the circuit must retain the same topology. You can stretch or shrink or change the shape of any connection, but you cannot remove or replace or make new connections - except in special circumstances.

A good first step, as used in the example which you cite, is to identify all the wires which are connected together. Then you can quickly draw each group of connections as a horizontal rail, and place all the circuit elements in vertical lines between the horizontal rails - as you might see them connected on an electronic 'breadboard'. See Redrawing Circuits for Clarity and Re-drawing Complex Schematics for examples. If there is a voltage or current source, this should connect the top and bottom rails. Alternatively, if you are trying to find an equivalent resistance between nodes A and B, place these on the top and bottom rails.

This example shows that what seems a difficult circuit can become obvious after re-drawing.


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