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

Step-by-step solution

Resistance, R = ρ l A R   α   l s a y   R e f f = l = 18 a s   l 1 = l 2 = l 3 = l / 3 ⇒ R 1 = R 2 = R 3 = R = 18 / 3 = 6 So from diagram 2 R = 12   a n d   R = 6 a l s o   w e   k n o w   R A B = R 2 R R R R 2 R + R R R A B = 6 × 12 6 + 12 = 4   Ω