Question

Six equal resistance of $1\Omega$ each are connceted to form the sides of a hexagon ABCDEF. If the equivalent resistance between A and D is $0.5N\Omega$, calculate the value of N.

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

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,
$\frac{1}{R}=\frac{1}{R_{ABCD}}+\frac{1}{R_{AFED}}=\frac{1}{3}+\frac{1}{3}$
$=\frac{2}{3}$
$\Rightarrow R=\frac{3}{2}\Omega =1.5\Omega$

Now,
$0.5N\Omega =1.5\Omega$
N = 3
Thus the value of N is 3.