question_answer

A wire of resistance \[{{V}_{C}}={{V}_{B}}\ne {{V}_{A}}\] is bent to form 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) \[{{V}_{C}}\ne {{V}_{B}}\ne {{V}_{A}}\]

B) \[{{V}_{C}}={{V}_{B}}={{V}_{A}}\]                           

C) \[\text{m}{{\text{s}}^{-1}}\]      

D)        \[\text{20m}{{\text{s}}^{-1}}\]

Correct Answer: A

Solution :

                Circumference of circle \[v=\frac{\omega }{k}=128\,\text{m}{{\text{s}}^{-1}}\] Resistance of wire \[\Rightarrow \] Resistance of each section \[\omega =v\times k=128\times 7.85\] \[y=A\sin (kx-\omega t)\]Equivalent resistance \[\therefore \]