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Asked by Prashant DIGHE | 18 Jul, 2019, 17:13: PM
answered-by-expert Expert Answer
The given resistor network is shown in fig.1.  If we connect a resistance x across C and D so that equivalent resistance
at terminals E and F due to resistances on right side also x, then this equivalent resistance value will continue
from right to left side till we reach terminals A and B.
 
Fig.2 shows the right side part of network at terminals E and F , resistance x is connected across C and D.
we need to choose the value of x so that equivalent resistance between E and F is x.
 
we have,  x = R(2R+x) / (3R +x )  ................(1)
 
By solving eqn.(1), we get x = (√3 - 1)R
 
Hence we have equivalent resistance at E and F due to resistances at right side is x = (√3 - 1)R.
 
If we replace all resistances at right side of E and F by x and calculate the equivalent resistance at G and H,
as explained above, equivalent resistance will be obtained is x .
 
This will continue towards left side after passing one unit of basic network till we reach terminals A and B.
 
Hence, if we connect (√3 - 1)R at C and D, then equivalent resistance between A and B is (√3 - 1)R.
 
This equivalent resistance is independent of number of items of resistances present in the network
Answered by Thiyagarajan K | 19 Jul, 2019, 12:24: PM

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