A wire of uniform resistance $\lambda\Omega/m$ is bent into a circle of radius $r$ and another piece

Question

A wire of uniform resistance $\lambda\Omega/m$ is bent into a circle of radius $r$ and another piece of wire with length 2 r is connected between points A and B $(AOB)$ as shown in figure. The equivalent resistance between points A and B is $\_\_\_\_$ $\Omega$.

Accepted Answer

$${\frac{1}{R_{AB}} = \frac{2}{\lambda\pi r} + \frac{1}{\lambda.2r} + \frac{2}{\lambda.3\pi r} }{= \frac{1}{\lambda r}\left\lbrack \frac{2}{\pi} + \frac{1}{2} + \frac{2}{3\pi} \right\rbrack }{= \frac{1}{\lambda r}\left( \frac{12 + 3\pi + 4}{6\pi} \right) = \frac{1}{\lambda r} \cdot \left( \frac{16 + 3\pi}{6\pi} \right) }{R_{AB} = \lambda r\left( \frac{6\pi}{16 + 3\pi} \right)}$$

Question

Options

Solution

More Current Electricity and Electrical Instrument Questions