Current Electricity 1 Question 8

8. A uniform metallic wire has a resistance of $18 \Omega$ and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is

(2019 Main, 10 Jan I)

(a) $12 \Omega$

(b) $8 \Omega$

(c) $2 \Omega$

(d) $4 \Omega$

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Solution:

  1. Resistance of each arm of equilateral triangle will be

$$ R=\frac{18}{3}=6 \Omega $$

So we have following combination will be

Equivalent resistance is

$$ \therefore \quad R _{A B}=\frac{12 \times 6}{12+6}=\frac{12 \times 6}{18}=4 \Omega $$



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