Seven resistors each of resistance 5 ohm are connected as shown in figure. The e

Question

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

Options:

A . 1 ohm

B . 7 ohm

C . 35 ohm

D . 49 ohm

Answer: Option B
:
B

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

5 i_{2} + 5 i_{3} - 10 i_{1} = 0

10 (i_{2} - i_{3}) - 5 (i_{1} + i_{3}) - i_{3} = 0

10 i_{1} + 5 (i_{1} + i_{3}) - E = 0

equation (i) and (ii) give

i_{2} = \frac{3 i_{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{2 E}{5 i_{1}}

from equation (iii) we have

E = 15 i_{1} + 5 i_{3} = \frac{35 i_{1}}{2}

R = \frac{2 E}{5 i_{1}} = \frac{2 * 35 i_{1}}{5 i_{1} * 2} = 7

Ohm

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