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Question

A wire of resistance $$4 R$$ is bent in the form of a circle. What is the effective resistance between the ends of the diameter?


Solution

When a wire of resistance $$4R$$ is bent in the form of circle, then the resistance of each segment across the diameter becomes $$2R$$ as shown in the figure.
Equivalent resistance between A and B: $$\dfrac{1}{R_{AB}} = \dfrac{1}{R_1} + \dfrac{1}{R_B}$$            (in parallel combination)
$$\therefore$$   $$\dfrac{1}{R_{AB}} = \dfrac{1}{2R} + \dfrac{1}{2R}$$ 

$$\dfrac{1}{R_{AB}} = \dfrac{2}{2R}$$                  

$$\implies$$  $$R_{AB} =R$$

636413_610092_ans.png

Physics

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