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Grade: 12
        


 


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.

10 years ago

Answers : (2)

AskiitianExpert Pramod-IIT-R
47 Points
							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.
						
10 years ago
Anurag Kishore
37 Points
							

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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9 years ago
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