Question

Each resistance in the adjoining network in of $1\Omega$. The effective resistance between A and B will be

• A. $\frac{4}{3}\Omega$
• B. $\frac{3}{2}\Omega$
• C. $7\Omega$
• D. $\frac{8}{7}\Omega$

Answer 1

Answer: (D)

$\frac{8}{7}\Omega$

Given : $R=1\Omega$

Equivalent circuit is shown above.

Equivalent resistance of path 1, $R_1=2R+(R\parallel 2R)$

$\therefore$ $R_1=2R+\frac{2R\times R}{2R+R}=\frac{8R}{3}$

Equivalent resistance of path 2, $R_2=R+R=2R$

$\therefore$ Equivalent resistance between A and B $R_{AB}=R_1\parallel R_2=\frac{R_1\times R_2}{R_1+R_2}=\frac{\left(8R/3\right)\times 2R}{\left(8R/3\right)+2R}=\frac{8}{7}R$

$⟹$ $R_{AB}=\frac{8}{7}\times 1=\frac{8}{7}\Omega$