Finding R equal in circuit

[tom_electronic]

hi all ,


in attached picture We want to find R equal

all Resistors are same and R = 1 ohm

how much we will measure AB resistance ?

R AB = ?

 

[MrAl]

Hi there,


This looks like an Inside/Outside symmetrical network of equal resistors, so i will
render a guess without calculating that because the horizontal and vertical
resistors do not conduct, the total resistance simplifies to 3/4 ohms (0.75 ohms).

 

[yusim]

This looks like an Inside/Outside symmetrical network of equal resistors

ok i dont know what an inside/outside network is so if i was givin this problem
id just do a bunch of y -> delta/ delta -> y conversions to get the answer

 

[MrAl]

Hi again,


The symmetricalness of a network helps to simplify the network considerably,
when it is in fact present. In most networks it is not present but in this network
symmetry is abundant. The direction of symmetry is from the 'inside' to the 'outside'
of the network, and so that means that many of the resistors are not conducting
because they are connected between two nodes of equipotential (due to the
symmetry). This puts the four diagonal legs in parallel, and of course the
three resistors that make up each leg in series. That's how we get 3/4...
3 because there are three resistors in series in each leg, and 4 because there are
four legs in parallel. The other resistors dont conduct.

 

[tom_electronic]

yes , R equal = 3/4