    Question

# The resistance of all the wires between any two adjacent dots is R. The equivalent resistance between A and B as shown in the figure is A
73R
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B
76R
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C
148R
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D
None of these
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Solution

## The correct option is C 76RSince we need to evaluate the resistance between A and B, therefore connect a power source between A and B as shown below. Since point D and E are connected to A by a wire of equal resistance, therefore both points D and E will be at equal potential. Hence we can neglect the resistance between D and E since no current will flow through it. The circuit can be redrawn as shown. For the branches CDG, EFH, GBI and BHJ, two equal resistances(R) are in series and their equivalent(2R) is in parallel with the third resistor(R). Hence the equivalent resistance for each branch will be Req1=2R×R2R+R=2R3 Hence the circuit reduces to the following circuit. Now the circuit is symmeteric about AB. For one side of AB say left, three resistances R, 2R/3 and 2R/3 are in series. Their equivalent resistance will be, Req2=R+2R3+2R3=7R3 Hence the circuit reduce to the one as shown below. Since two equal resistance are connected across AB in parallel, there equivalent resistance will be, RAB=12(7R3)=7R6 Hence option B is correct.  Suggest Corrections  1      Similar questions  Related Videos   Series and Parallel Combination of Resistors
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