Question

The equivalent resistance between the points A and B in the adjoining figure will be

• A. $2.63\Omega$
• B. $3.71\Omega$
• C. $1.68\Omega$
• D. $5.12\Omega$

Answer 1

Answer: (A)

$2.63\Omega$

By using the star delta transformation shown by figure 1 to figure 2.
We know that $R_1=\frac{r_1\times r_3}{r_1+r_2+r_3}$
$R_1=\frac{5}{8}\Omega$
$R_2=\frac{r_1\times r_2}{r_1+r_2+r_3}$
$R_2=\frac{2}{8}$
$R_3=\frac{r_3\times r_2}{r_1+r_2+r_3}$
$R_3=\frac{10}{8}$
Now the equivalent resistance from figure 2
$=R_1+\frac{1}{\frac{1}{R_2+r_4}+\frac{1}{R_3+r_5}}$
$=\frac{5}{8}+\frac{1}{\frac{1}{\frac{2}{8}+3}+\frac{1}{\frac{10}{8}+4}}\Omega$
$=2.63\Omega$