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11.10 Equivalent Resistance of Network

There are many techniques to find equivalent or effective resistance between any two terminals of a network. A special skills is to be developed to decide which technique would be easier to use for the given network.

11.10.1 Wheatstone Bridge

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The bridge is balanced. Under balanced condition, points B and D are at same potential and no current flows through the resistance G. Therefore, while calculating the equivalent resistance between A and C, the resistance G is not considered. It is interesting to note that under balanced conditions, the points B and D may be treated as shorted, so that the equivalent circuit becomes as shown. The equivalent resistance between A and C is then given as

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11.10.2 Chain of Dissolving Loops

In general, the equivalent resistance of such a network is given by solving end loop and then same pattern is obtained as that of original network.

11.10.3 Chain of Infinite Loops

The figure represents chain of infinite loops. In this network, we have to find the equivalent resistance between A and B.

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In this case, if we remove the first repeating unit, then the network reduces to a pattern as shown below. Since the pattern extends upto infinity, therefore, removing one loop from it does not affect the equivalent resistance. That is, if R0 is the equivalent resistance between A and B, then the equivalent resistance between C and D is also R0.

Thus, the network reduces to

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11.10.4 Method of Mirror Image

Let current enters a circuit through point A and leaves it from point B. If we can draw an imaginary line connecting A and B in such a way that this line divides the circuit into two halves such that one half is mirror image of the second half with respect to this imaginary line, then we can consider these two halves as independent of each other without being connected at any point on the above imaginary line other than the points A and B.

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