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Asked by patelnamra608 | 26 Jan, 2024, 11:01: AM

Let us assume a potential difference V is applied between A and B as shown in figure.

Let i be the current drawn by the given resistor network .

At point C , input current i is split into i1 and i2 . By symmetry at H , i1 and i2 combine to give i .

At point D , current i2 is split into i3 and i4 . By symmetry at G , i3 and i4 combine to give i2 .

At point E , current i1  and i3 combine to give current i5. By symmetry at F , current i5 is split into i1 and i3 .

By applying Kirchoff's voltage law to the loop CIJEC , we get

;  Hence we get ,   ............................. (1)

Similarly by applying Kirchoff's voltage law to the loop DEFGMND , we get

..............................(2)

By applying Kirchoff's voltage law to ACDEFGHBOPA , we get

Hence we get from above expression ,

............................(3)

Using eqn.(1) , we get from above equation as

............................(4)

By substituting i5 in eqn.(2) , we get

.........................(5)

At junction E , by applying Kirchoff's current law , we get

Using eqn.(4) and (5) , we get current i1 from above expression as

By substituting i3 and i5 in eqn.(3) , we get

Hence total current drawn by given resistor network is

Hence the effective resistance between points A and B is (r/2)

Answered by Thiyagarajan K | 26 Jan, 2024, 08:47: PM

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