Question

The resistance of a wire is ${10}^{-6}\Omega /meter$. This wire is turned in the form of a circle of diameter $2m$. A piece of same materials is connected at this diameter. The resultant resistance across the diameter $AB$ will be:

• A. $0.88\times {10}^{-6}\Omega$
• B. $14\pi \times {10}^{-6}\Omega$
• C. $\frac{4}{3}\pi \times {10}^{-6}\Omega$
• D. $\frac{2}{3}\pi \times {10}^{-6}\Omega$

Answer 1

The correct option is A $0.88\times {10}^{-6}\Omega$

$d=2m$

$r=1m$

$2\pi r=2\pi m$

$R_1={10}^{-6}\times \pi r$

$={10}^{-6}\pi \Omega$

$R_3={10}^{-6}\pi \Omega$

$R_2={10}^{-6}\times 2$

$=2\times {10}^{-6}\Omega$

$\frac{1}{R_{AB}}=\frac{1}{\pi \times {10}^{-6}}+\frac{1}{2\times {10}^{-6}}+\frac{1}{\pi \times {10}^{-6}}$

$={10}^6[\frac{2}{\pi }+\frac{1}{2}]$

${10}^6\left[\frac{4+\pi }{2\pi }\right]$

$R_{AB}=\left(\frac{2\pi }{\pi +4}\right)\times {10}^{-6}\Omega$

$=0.88\times {10}^{-6}\Omega$