How to solve the following circuit of resistors?

Question

Twelve resistors each of resistance 1 Ω are connected in the circuit shown in the adjoining figure. Net resistance between points A and H would be :-

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Answer 1 · 2018-04-01T14:16:12

$3/4 Omega$

By symmetry, the currents in the resistors must be distributed as shown below

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Applying Kirchoff's Voltage law to the loop ACEBA gives :

$y+z-x/2-x = 0 implies y+z=3/2 x$

while the loop CHGEC gives

$y-z-(x+2z)-(x/2+z)-z = 0 implies y-4z = 3/2x$

The two equations together give $z=0$ and so

$y = 3/2x implies I = 2y+x = (2+2/3)y = 8/3y implies y = 3/8I$

The net voltage drop across thee circuit = the voltage drop along the path ACH =

$2y times 1\ Omega = 3/4I times 1 Omega$

Thus, the effective resistance between A and H is $3/4 Omega$