A wire of length l is bent into the form of an equilateral triangle. The effective resistance between any two vertices of the triangle is R. If the same wire is bent in the form of a square, what will be the effective resistance between the ends of one side?
Answers
Answer:
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Explanation:
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Effective resistance between the ends of one side of square = 3/4R.
Explanation:
Given: A wire of length l is bent into the form of an equilateral triangle. The effective resistance between any two vertices of the triangle is R.
Find: If the same wire is bent in the form of a square, what will be the effective resistance between the ends of one side?
Solution:
We know that electrical resistance R = pL/A where L is the length and A is the cross-sectional area.
The same wire is bent differently, here the p and A will remain the same.
R is directly proportional to length. So when length is reduced, Resistance will also reduce.
Let R be the resistance when the shape is triangle and R2 be the resistance when shape is square.
Length is L in equilateral triangle, let total length of wire be 3L.
Now the same wire is arranged as a square. So each side will be 3/4L.
Resistance of a side of square R2 = p 3/4L / A= 3/4 * pL/A = 3/4R
Effective resistance between the ends of one side of square = 3/4R.