A wire of resistance 10 , Omega is bent in th | vedclass

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Question

(A) When a wire of resistance $10 \, \Omega$ is bent into a circle,the total resistance is distributed uniformly along the circumference.Any diameter

Vedclass · Accepted Answer

$2.5 \, \Omega$

Vedclass · Answer

(A) When a wire of resistance $10 \, \Omega$ is bent into a circle,the total resistance is distributed uniformly along the circumference.Any diameter divides the circle into two equal semicircular parts.Each semicircle will have a resistance of $R_1 = R_2 = 10 / 2 = 5 \, \Omega$.These two semicircular parts are connected in parallel between the two ends of the diameter.The effective resistance $R_{eq}$ is given by the formula for parallel resistors: $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$.Substituting the values: $\frac{1}{R_{eq}} = \frac{1}{5} + \frac{1}{5} = \frac{2}{5}$.Therefore,$R_{eq} = \frac{5}{2} = 2.5 \, \Omega$.

$A$ wire of resistance $10 \, \Omega$ is bent in the form of a closed circle. What is the effective resistance between the two points at the ends of any diameter of this circle?

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