Question

Six equal resistance of $1\Omega$ each are connceted to form the sides of a hexagon ABCDEF. Calculate the resistance offered by the combination if the current enters at A and leaves at D.

• A. $1\Omega$
• B. $1.5\Omega$
• C. $2\Omega$
• D. $2.5\Omega$

Answer 1

The correct option is B $1.5\Omega$

Given:
Six resistors each of value =$1\Omega$

Resistance of the branch ABCD,
$R_{ABCD}=(1+1+1)\Omega R_{ABCD}=3\Omega$
Similarly, resistance of the branch AFED,
$R_{AFED}=(1+1+1)\Omega R_{AFED}=3\Omega$
Since $R_{ABCD}$ and $R_{AFED}$ are in parallel, the required resistance is given by,
$\frac{1}{R}=\frac{1}{R_{ABCD}}+\frac{1}{R_{AFED}}=\frac{1}{3}+\frac{1}{3}$
$=\frac{2}{3}$
$\Rightarrow R=\frac{3}{2}\Omega =1.5\Omega$