question_answer

The resistance of a wire is \[{{10}^{-6}}\Omega \] per metre. It is bend in the form of a circle of diameter \[2\,m\]. A wire of the same material is connected across its diameter. The total resistance across its diameter AB will be

A)            \[\frac{4}{3}\pi \times {{10}^{-6}}\Omega \]             

B)            \[\frac{2}{3}\pi \times {{10}^{-6}}\Omega \]

C)            \[0.88\times {{10}^{-6}}\Omega \]                                 

D)            \[14\pi \times {{10}^{-6}}\Omega \]

Correct Answer: C

Solution :

                   Resistance across \[AB=\frac{1}{R'}=\frac{1}{R}+\frac{1}{R}+\frac{1}{{{R}_{1}}}\] \[{{R}_{1}}=2\times {{10}^{-6}}\Omega \] and \[R=\pi \times 1\times {{10}^{-6}}\Omega \] On solving, \[R'=0.88\times {{10}^{-6}}\Omega \]