Question

A wire of resistance 12 ohms per meter is bent to form a complete circle of radius 10 cm. The resistance between its two diametrically opposite points, A and B as shown in the figure is

• A. $\rho$
• B. $\frac{r_{1}}{r_{2}}\frac{\rho}{2}$
• C. $\frac{r_{2} - r_{1}}{r_{1}r_{2}}\frac{\rho}{4\pi}$
• D. $\frac{r_{1}r_{2}}{r_{2} - r_{1}}\frac{\rho}{4\pi}$

Answer 1

Answer: (D)

$\frac{r_{1}r_{2}}{r_{2} - r_{1}}\frac{\rho}{4\pi}$

Answer 2

: Wire of length $2\pi \times 0.1$m of $12\Omega m^{- 1}$is bent to a circle.

Resistance of each part $= 12 \times \pi \times 0.1$

$= 1.2\pi\Omega$

$\therefore$Total resistance $= 0.6\pi\Omega.$