Question

The effective resistance across the points $A$ and $I$ is

• A. $2\Omega$
• B. $1\Omega$
• C. $0.5\Omega$
• D. $5\Omega$

Answer 1

Answer: (B)

Since the potential at $B,G$ is same, the potential at $C$ $H$ and $F$ is same and the potential at $D$ and $E$ is same.
$\therefore$ The circuit can be reduced to

The equivalent resistance of (i) is
$\frac{1}{R_1}=\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}=\frac{4}{2}=\frac{2}{1}$ or $R_1=\frac{1}{2}\Omega$
The equivalent resistance of (II) is
$\frac{1}{R_2}=\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}=\frac{4}{2}=\frac{2}{1}$ or $R_2=\frac{1}{2}\Omega$
The effective resistance between $A$ and $I$ is
$R_{eff}=R_1+R_2=\frac{1}{2}+\frac{1}{2}=1$ or $R_{eff}=1\Omega$