Question

Seven resistors each of resistance 5 ohm are connected as shown in figure. The equivalent resistance between points A and B is

• A. 1 ohm
• B. 7 ohm
• C. 35 ohm
• D. 49 ohm

Answer 1

The correct option is B 7 ohm

The circuit can be redrawn as shown in figure. Let a bettery of emf E and of negligible resistance be connected as shown. The current in various branches are shown.Applying Kirchoff's second law to loops ACDA,CBDC and ADBGFA we have
$5i_2+5i_3-10i_1=0$
$10(i_2-i_3)-5(i_1+i_3)-i_3=0$
$10i_1+5(i_1+i_3)-E=0$
equation (i) and (ii) give $i_2=\frac{3i_1}{2}$ and $i_3=\frac{i_1}{2}.$ If R is the effective resistance between A and B
then $R=\frac{E}{i_1+i_2}=\frac{2E}{5i_1}$
from equation (iii) we have
$E=15i_1+5i_3=\frac{35i_1}{2}$
$R=\frac{2E}{5i_1}=\frac{2\ast 35i_1}{5i_1\ast 2}=7$ Ohm