Question

A and B are two points on a uniform ring of resistance $15\Omega$. The $\angle$AOB$={45}^o$ where O is the centre of the ring. The equivalent resistance between A and B is?

• A. $1.64\Omega$
• B. $2.84\Omega$
• C. $4.57\Omega$
• D. $2.64\Omega$

Answer 1

Answer: (A)

$1.64\Omega$

The resistance between the points A and B is

$R_1=\frac{\frac{\pi }{4}}{2\pi }\times 15$

Since the region between the A and B has $\pi /4$ part of the $2\pi$ angle of the circle.

$=\frac{1}{8}\times 15=\frac{15}{8}$

The resistance of the remaining part:

$R_2=\frac{7\pi }{8\pi }\times 15=\frac{105}{8}$

These two resistances are parallel to each other. Therefore,

$R_{net}=\frac{\frac{15}{8}\times \frac{105}{8}}{\frac{15}{8}+\frac{105}{8}}$

$=\frac{105}{8}\times \frac{15}{8}\times \frac{8}{120}=\frac{105}{64}=1.64\Omega$