Question

An equilateral triangle has been constructed with an uniform wire whose resistance per unit length is $4$ ohm $c{m}^{-1}$. If the length of each side of the triangle is $10$c, the resistance across any side will be.

• A. $80$ ohm
• B. $40$ ohm
• C. $\frac{80}{3}$ ohm
• D. $\frac{40}{3}$ ohm

Answer 1

The correct option is C $\frac{80}{3}$ ohm

$\frac{R}{l}=4$ ohm/cm

$R=$ Resistance of each side

$l=10cm$

$R=4\times 10=40$ ohm

In a triangle two sides are in series and parallel to third one.

So total resistance is $\cfrac{1}{R_t}=\cfrac{1}{40+40}+\cfrac{1}{40}=\cfrac{80}{3}

$R_t=\frac{80}{3}$ ohm