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Q : As shown in Fig. an equilateral triangle has resistance of outermost sides as R each. Further there exists infinite no. of Equilateral triangles in it . Each arm of the triangle inside the outermost triangle has resistance R/2, and it continues to all inner triangles as..R/4,R/8..so on.Find the Equivalent resistance between Point A and B.


 


Q: As shown in Fig. an equilateral triangle has resistance of outermost sides as R each. Further there exists infinite no. of Equilateral triangles in it . Each arm of the triangle inside the outermost triangle has resistance R/2, and it continues to all inner triangles as..R/4,R/8..so on.Find the Equivalent resistance between Point A and B.

Grade:12

2 Answers

AskiitianExpert Pramod-IIT-R
47 Points
11 years ago
At every point the resistors meet would be effectively increasing the resistance. It is because any current here would only be able to see the outer path due to the presence of infinite number of triangular mesh. The outer path consists of two resistors with resistance of R each. They are in series and thus, the resultant resistance would be R+R = 2R. This is the effective resistance for such a complicated mesh.
Anurag Kishore
37 Points
11 years ago

Hi

Let equivalent resistance be x

Circuit is as shown

Req = 2R(R+x)/(4R+3x)   ----------------------(1)

but we assumed Req = x  ----------------------(2)

So from 1 and 2

x = R(71/2 - 1)/3

 

This is the only way to solve these type of questions

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