A uniform wire of resistance 4 Omega is bent | vedclass

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(A) The total resistance of the wire is $R = 4 \ \Omega$. When the wire is bent into a semicircle,it is divided into two equal halves,each having a re

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(A) The total resistance of the wire is $R = 4 \ \Omega$. When the wire is bent into a semicircle,it is divided into two equal halves,each having a resistance of $R' = R/2 = 4/2 = 2 \ \Omega$.These two halves are connected in parallel between the two ends of the diameter.The equivalent resistance $R_{eq}$ of two resistors $R_1$ and $R_2$ in parallel is given by $1/R_{eq} = 1/R_1 + 1/R_2$.Here,$R_1 = 2 \ \Omega$ and $R_2 = 2 \ \Omega$.Therefore,$1/R_{eq} = 1/2 + 1/2 = 1 \ \Omega^{-1}$.Thus,$R_{eq} = 1 \ \Omega$.

$A$ uniform wire of resistance $4 \ \Omega$ is bent into the shape of a semicircle. What is the equivalent resistance between the two ends of the diameter (in $\Omega$)?

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