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(C) The resistance $R$ of a wire is given by the formula $R = \rho \frac{l}{A}$, where $\rho$ is the resistivity (specific resistance), $l$ is the len

Vedclass · Accepted Answer

$0.024$

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(C) The resistance $R$ of a wire is given by the formula $R = ho \frac{l}{A}$, where $ho$ is the resistivity (specific resistance), $l$ is the length, and $A$ is the cross-sectional area.Given: $ho = 64 	imes 10^{-6} \, \Omega \cdot 	ext{cm}$, $l = 198 \, 	ext{cm}$, $R = 7 \, \Omega$.The area of the cross-section $A = \pi r^2$, where $r$ is the radius.Substituting the values into the formula: $7 = (64 	imes 10^{-6}) 	imes \frac{198}{\pi r^2}$.Using $\pi \approx \frac{22}{7}$, we get: $7 = \frac{64 	imes 10^{-6} 	imes 198}{(22/7) 	imes r^2}$.$r^2 = \frac{64 	imes 10^{-6} 	imes 198 	imes 7}{7 	imes 22} = \frac{64 	imes 10^{-6} 	imes 198}{22} = 64 	imes 10^{-6} 	imes 9 = 576 	imes 10^{-6}$.Taking the square root: $r = \sqrt{576 	imes 10^{-6}} = 24 	imes 10^{-3} = 0.024 \, 	ext{cm}$.

$A$ metal wire of specific resistance $64 \times 10^{-6} \, \Omega \cdot \text{cm}$ and length $198 \, \text{cm}$ has a resistance of $7 \, \Omega$. The radius of the wire will be ............. $\text{cm}$.

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