Question
A wire of resistance 12 ohms per meter 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 wire of resistance 12 ohms per meter 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.
$$3\Omega $$
B.
$$6\pi \Omega $$
C.
$$6\Omega $$
D.
$$0.6\pi \Omega $$
Answer :
$$3\Omega $$
Solution :
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 $$R = \frac{{6 \times 6}}{{12}} = 3\Omega $$
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 $$R = \frac{{6 \times 6}}{{12}} = 3\Omega $$
