question_answer

A wire of resistance 12 ohms per meter is bent to from a complete circle of radius 10 cm. The resistance between its two diametrically opposite points, A and B as shown in the figure, is

A) \[3\Omega \]                 

B)        \[6\pi \Omega \]

C) \[6\Omega \]                 

D)        \[0.6\pi \Omega \]

Correct Answer: A

Solution :

[a] The resistance of length \[2\pi R\] is \[12\Omega \]. Hence the resistance of length \[\pi R\] is \[6\Omega .\]. Thus two resistances of \[6\Omega \] can be represented as shown in fig. 2. \[\therefore \] Equivalent resistance \[R=\frac{6\times 6}{12}=3\Omega \]