Short cut tricks to find resistance of large/messed resistance's network.

[vkash]

Today our physics teacher teach us how to find resistance of a network of resistance that is messed to heavily(example all sides of a cube are resistance find resistance). Ok those are very good methods, but it seems that they are not result of experiments done by genius persons it seems that they are derived from Kirchoff's laws of loops. Can you please tell me the proof or something like this for their tricks these short cut tricks.
these short ct tricks are

(1)If in a network of resistances line joining terminals in an axis of symmetry then
(a) corresponding same point will carry same current.
(b) If network is folded about this axis of symmetry then equivalent resistance does not change.
(2)If in a network of resistances the perpendicular bisector of joining terminals is axis of symmetry then
(a) corresponding points will have same current but their directions will be different with respect to axis of
symmetry.
(b) If a resistance is lying on the axis of symmetry then it can removed without changing equivalent
resistance.
(c) all the points lying on this point will have same potential.
(3) If in network of resistances if all the resistances are became n times then net resistance will n times.

I don't ask him(teacher) for these proofs/derivations because like every time he will say " Proofs never come in examination so what's gain of learning those proofs or derivations."
After all i hope you will not reply so.

thanks for reading. make reply if you know anything about it.double thanks to repliers.

 

[vkash]

Does non of you know it's answer??
If their is any problem understanding question then tell me i will try to make it clear.

 

[vkash]

Does non of you know it's answer??
If their is any problem understanding question then tell me i will try to make it clear.

I post it here bcz i thought there are some persons whichc will think on it. I think none of you think.Howeveri think a bit and want to share it with you.
explanation for
1(a) let us assume that there is different current in upward upper and lower part of circuit. Now just reverse the direction of the circuit i mean upper part in lower and lower in upper. So the current slowing in upper part will now the current in lower part and current flowing in lower part willl in upper part. BUT the circuit is same as it was before reversing. So here arise contradiction which can killed if and only current in upper and lower region will same.
1(b) still now i have no idea for this.
2(a) It is much similar to 1(a) but in this case we require to revert the direction of current. If we take current different then contradiction will arise which can be cured only by taking current similar.
2(b) It is derivative of 2(a)
2(c) doesn't get;
2(d) One more thing that i can't explain.

hey friends please help yar;Tell me something that how it can.

 

[Studiot]

(b) If a resistance is lying on the axis of symmetry then it can removed without changing equivalent
resistance.

Perhaps you should have another chat with your advisor?

Look at the following circuit and ask yourself if the equivalent resistance between A and B is unaffected by removing R_s.

go well

 

[vkash]

Perhaps you should have another chat with your advisor?

Look at the following circuit and ask yourself if the equivalent resistance between A and B is unaffected by removing R_s.

go well

This is wheat stone bridge. It is not affected by R_s.But think this is not the way of explaining any thing. I mean 2*2=4 and2+2=4. It does not mean that * is same as +.
How you can explain all the phenomena by one example. It's particular case.