A piece of wire of resistance 4,Omega is bent | vedclass

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(B) The original wire has a resistance of $R = 4\,\Omega$. When the wire is bent at its mid-point,it is divided into two equal halves,each having a re

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(B) The original wire has a resistance of $R = 4\,\Omega$. When the wire is bent at its mid-point,it is divided into two equal halves,each having a resistance of $R' = \frac{R}{2} = \frac{4}{2} = 2\,\Omega$. When these two halves are twisted together,they form a parallel combination. The equivalent resistance $R_{eq}$ of two resistors in parallel is given by $\frac{1}{R_{eq}} = \frac{1}{R'} + \frac{1}{R'}$. Substituting the values,$\frac{1}{R_{eq}} = \frac{1}{2} + \frac{1}{2} = 1$. Therefore,$R_{eq} = 1\,\Omega$.

$A$ piece of wire of resistance $4\,\Omega$ is bent through $180^o$ at its mid-point and the two halves are twisted together. The new resistance is ............ $\Omega$.

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