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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
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B
7 ohm
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C
35 ohm
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D
49 ohm
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Solution

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
5i2+5i310i1=0
10(i2i3)5(i1+i3)i3=0
10i1+5(i1+i3)E=0
equation (i) and (ii) give i2=3i12 and i3=i12. If R is the effective resistance between A and B
then R=Ei1+i2=2E5i1
from equation (iii) we have
E=15i1+5i3=35i12
R=2E5i1=235i15i1 2=7 Ohm


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