Question

what is total resistance, between A and B in the circuit shown in the given figure

Answer 1

Resistance of AF and FE are in series. So total = 2+2 = 4 ohm
Now it is in parallel with AE(4 ohm).
So effective resistance between A and E is $\frac{1}{1/4+1/4} = \frac{1}{2/4} =4/2=2$ ohm.

Now it is in series with ED(2 ohm). So total = 4 ohm which is in parallel with AD(4 ohm). So effective resistance between A and D is 2 ohm.

It goes on and finally the effective resistance between A and B is 2 ohm.

Answer 2

effective resistance between A and B:

Resistance along AFE:  4 ohms.
it is in parallel with 4 ohms along AE.  Hence, effective resistance of these two:
        = 4 * 4 /(4+4) = 2 ohms

resistance along AED: 2 ohms + 2 ohms = 4 ohms.
This is in parallel with the resistance along AD : 4 ohms.

Hence the effective resistance :  2 ohms .
This is in series with resistance 2 ohms along CD.  HEnce, total resistance along ADC is 4 ohms.

This is parallel with the 4 ohms resistance along AC.  Effective resistance then is 2 ohms.  This is in series with 2 ohms along BC.
Hence the along ACB the resistance is 4 ohms.
Between A and B there are two  4 ohms resistances in parallel.

Hence, effective resistance between A and B = 2 ohms.


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effective resistance between A and D:

Total resistance along ABC = 6 ohms.
Between A and C we have  4 ohms and 6 ohms in parallel.
equivalent Resistance between A & C along AC:   6*4/(6+4) = 2.4 ohms
Add this to the resistance 2 ohms between C and D.  Hence, Along ACD the resistance is 4.4 ohms.

similarly, on the other side, Equivalent resistance along AED will be 4.4 ohms, from symmetry.

Now, 4 ohms between A and D, 4.4 ohms along AED,  and  4.4 ohms along ACD are all in parallel.

equivalent resistance along AD:   R  (say).
   1/ R = 1/4 + 1/4.4 + 1/4.4 =  (1.1 +1+1)/4.4 = 3.1/4.4
      R  =  4.4 / 3.1 ohms = 1.42  ohms.