Find the equivalent resistance between points `A` and `B` in the following circuits?

Answer

A, B, C, D

Explanation

a.

b.balanced Wheatstone bridge in parallel with `R`.
d.
e.

Let us take current of `10 A` between `A` and `B`
Loop equation in loop 1
`-2i_1-2(i_1-i_2)+4(10-i_1_)=0` ..........i
Loop equation in loop 2
`-8i_2+10(10-i_2)+2(i_1-i_2)=0`.......ii
Solving these two equatioins we get
`i_1=6.53 A and i_2=6.11A`
Now let us find `V_(AB)` across path `ACB`,
`V_(AB)=2i_1+8i_2=61.94V`
Now, `V_(AB)=i_("net")R_("net")=(10)R_(net)`
`:. 61.94=10R_("net")`
or `R_("net")=6.194Omega`
f.Two resistors wheatstone bridge, in parallel with `1 Omega` resistance between points `A` and `B`.
The encircled resistance of `2Omega` can be removed from the Wheatstone bridge.

One resistor of `2Omega` has already from the original circuit given the question. As its two ends will be the same potential (by symmetry)