Question

find the equivalent resistance Across ab with r=3

Answer 1

i think your answer but am not sure sorry ♥♥♥♥♥❤❤❤❤♥♥♥♥♥♥❤❤❤What is the equivalent resistance across AB in the circuit (attached in details)?

One of the possible approaches would be to consider converting the middle star connection of 2 ohm resistors into a delta connection.

The generic proof and relevant equations for conversion of start to delta and vice versa can be seen in this page :

So from the same,

since the resistance of all the arms of the star are same, we can get:

Rdelta=2∗2+2∗2+2∗22=6

now,

two of the 6 ohm resistances are in parallel with 1 ohm each, and that will be in parallel to the third 6 ohm resistor which will be on the side of the battery.

Thus the parallel resistance of each of the 6ohm parallel with 1 ohm branch becomes:

Rparallel=6∗16+1=67ohm

Now those two 6/7 ohm resistances are in series with each other and in parallel to the 6 ohm resistor on the side of the battery.

So the series resistance becomes:

Rseries=67∗2=127

Now for the parallel connection with the 6 ohm,

Rparallel2=127∗6127+6=43ohm

Now finally that is in series with the 1 ohm resistor

Therefore,

RAB=43+1=7/3ohm=2.33ohm