Question

A circular conductor is made of a uniform wire of resistance 2 x ${10}^{-3}$ ohm/metre and the diameter of this circular conductor is 2 metres. Then the resistance measured between the ends of the diameter is (in ohms)

• A. $\pi \times {10}^{-3}$
• B. $2\pi \times {10}^{-3}$
• C. $4\pi \times {10}^{-3}$
• D. $4\times {10}^{-3}$

Answer 1

The correct option is A $\pi \times {10}^{-3}$

The resistance per unit length is given to be $R^{\prime }=2\times {10}^{-3}$
The length can be calculated as $L=\pi \times D$, where D is given diameter of 2 m.
Hence $L=2\pi$
Therefore,

Resistance $=2\times {10}^{-3}\times 2\pi =4\pi \times {10}^{-3}Ohms.$

Now when the resistance is measured between ends of any diameter, it can

be seen as parallel connection of two resistances R/2 each (R being the total

resistance of the entire loop). So the resistance between two end points of a diameter will be R/4 i.e. $\pi \times {10}^{-3}Ohms.$