Question

In the given star network the equivalent resistance between A and F is

• A. 1.944 R
• B. 0.973 R
• C. 0.486 R
• D. 0.243 R

Answer 1

Answer: (B)

0.973 R

In the given star network to find the resistance of the branch BJ, draw a line AL perpendicular to BJ.
Hence, $BJ=2LJ=2R\cos {72}^{\circ }$

$BJ=0.62R$

Now, the resistance $R_B$(say) of branch BCD is,

$R_B=\frac{2R\times \left(0.62\right)R}{2R+\left(0.62\right)R}$

$R_B=\frac{1.24R}{2.62}$

The resistance $R_B$ is same for branches DEF, FGH, HIJ.

The circuit can be converted into a balanced Wheatstone bridge as shown in the figure.

Hence, the net resistance in AF $R_{AF}$(say) is given by,

$R_{AF}=\frac{R+R_B}{2}$

$R_{AF}=0.973R$