A wire of resistance $R$ is cut into 8 equal pieces. From these pieces two equivalent resistances ar

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A wire of resistance $R$ is cut into 8 equal pieces. From these pieces two equivalent resistances are made by adding four of these together in parallel. Then these two sets are added in series. The net effective resistance of the combination is:

Accepted Answer

After being cut into 8 equal pieces,⇒ Resistance of each piece $= R^{'} = \frac{R}{8}$Each set has 4 pieces in parallel combination⇒ Resistance of each set $= R^{''} = \frac{R^{'}}{4} = \frac{R}{32}$Both sets are connected in series$$	herefore\ R_{	ext{eq}	ext{~}} = R^{''} + R^{''} = 2 	imes \frac{R}{32} = \frac{R}{16}$$

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