Question

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is

(1) \(9 / 8\)

(2) \(8 / 9\)

(3) \(27 / 32\)

(4) \(32 / 27\)

Answer 1

Correct option is : (4) \(32 / 27\) 

\(R=\frac{\rho \ell}{A}\) 

So, \(\mathrm{R} \ \alpha \ \ell\) 

Side length of triangle is \(1 / 3\) of total length.

 

 

\(\left(R_{e q}\right)_{1}=\frac{2 r / 3 \times r / 3}{2 r / 3+r / 3} \quad\left(R_{e q}\right)_{2}=\frac{3 r / 4 \times r / 4}{3 r / 4+r / 4}\) 

\( \left(R_{\text {eq }}\right)_{1}=2 r / 9\quad \left(\mathrm{R}_{\mathrm{eq}}\right)_{2}=3 \mathrm{r} / 16\) 

\(\frac{\left(\mathrm{R}_{\mathrm{eq}}\right)_{1}}{\left(\mathrm{R}_{\mathrm{eq}}\right)_{2}}=\frac{2 \mathrm{r} / 9}{3 \mathrm{r} / 16}=\frac{32}{27}\)