A wire of resistance 3Ω is cut into three equal pieces, which are joined to form a triangle. The equivalent resistance between any two corners of the triangle is :

Question

A wire of resistance 3Ω is cut into three equal pieces, which are joined to form a triangle. The equivalent resistance between any two corners of the triangle is : (A) (3/2)Ω (B) (2/3)Ω (C) (1/4)Ω (D) 4 Ω

Tardigrade Admin · Accepted Answer

It will be a case of one resistance of 1 Ω connected in parallel with two resistance in serice each of 1 Ω . Hence (1/Rp) =(1/1) + (1/2) = (3/2) . i.e. Rp = (2/3)

Q. A wire of resistance $3Ω$ is cut into three equal pieces, which are joined to form a triangle. The equivalent resistance between any two corners of the triangle is :

$\frac{3}{2} Ω$

$\frac{2}{3} Ω$

$\frac{1}{4} Ω$

$4Ω$

It will be a case of one resistance of 1 $Ω$ connected in parallel with two resistance in serice each of 1 $Ω$ . Hence $\frac{1}{R _{p}} = \frac{1}{1} + \frac{1}{2} = \frac{3}{2}$ .
$i . e . R_{p} = \frac{2}{3}$

Q. A wire of resistance 3Ω is cut into three equal pieces, which are joined to form a triangle. The equivalent resistance between any two corners of the triangle is :

23​Ω

32​Ω

41​Ω

4Ω