Question

Calculate the equivalent resistance between the points $A$ and $B$ for the following combination of resistors:

Answer 1

Let $4\Omega$, $4\Omega$ and $4\Omega$ are in series.
$R_1=4+4+4=12\Omega$
Now $2\Omega$, $2\Omega$ and $2\Omega$ are in series.
$R_2=2+2+2=6\Omega$
Now, $R_1=12\Omega$, $R_2=6\Omega$ and $4\Omega$ are in parallel.
$\frac{1}{R_3}=\frac{1}{12}+\frac{1}{4}+\frac{1}{6}$
$=\frac{1+3+2}{12}=\frac{6}{12}=\frac{1}{2}$
$R_3=2\Omega$
Now between $A$ and $B$, $5\Omega$, $2\Omega$ and $6\Omega$ are in series.
Resistance between $A$ and $B$, $R=5+2+6=13\Omega$
Hence, Equivalent resistance between $A$ and $B$ $=13\Omega$