Question

Twelve resistors each of resistance $16\,\Omega$ are connected in the circuit as shown. The net resistance between $A$ and $B$ is

• A. $1\,\Omega$
• B. $2\,\Omega$
• C. $3\,\Omega$
• D. $4\,\Omega$

Answer 1

Answer: (D)

$4\,\Omega$

Answer 2

The equivalent circuit is shown in figure.
The equivalent resistance of each parallel branch is
$R_{P}=R\|R\| R=(1 / R+1 / R+$ $1 / R)^{-1}=R / 3$
Thus, net resistance is
$R_{\text {net }}=(R / 3+R / 3+R / 3)\|(R / 3)=R\|(R / 3)$
$=\frac{R \times R / 3}{R+R / 3}=R / 4=16 / 4=$
$4\, \Omega$