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(A) Given: Dimensions $l_1 = 50 \ cm = 0.5 \ m$,$A_1 = 1 \ cm 	imes 1 \ cm = 10^{-4} \ m^2$. Resistivity $ho = 3.5 	imes 10^{-5} \ \Omega \cdot m$

Vedclass · Accepted Answer

$17.5 	imes 10^{-2} \ \Omega, 7 	imes 10^{-6} \ \Omega$

Vedclass · Answer

(A) Given: Dimensions $l_1 = 50 \ cm = 0.5 \ m$,$A_1 = 1 \ cm 	imes 1 \ cm = 10^{-4} \ m^2$. Resistivity $ho = 3.5 	imes 10^{-5} \ \Omega \cdot m$.Case $1$: Resistance between square ends $(l = 0.5 \ m, A = 10^{-4} \ m^2)$:$R_1 = ho \frac{l}{A} = 3.5 	imes 10^{-5} 	imes \frac{0.5}{10^{-4}} = 3.5 	imes 0.5 	imes 10^{-1} = 1.75 	imes 10^{-1} = 17.5 	imes 10^{-2} \ \Omega$.Case $2$: Resistance between rectangular ends $(l = 1 \ cm = 0.01 \ m, A = 1 \ cm 	imes 50 \ cm = 50 \ cm^2 = 50 	imes 10^{-4} \ m^2)$:$R_2 = ho \frac{l}{A} = 3.5 	imes 10^{-5} 	imes \frac{0.01}{50 	imes 10^{-4}} = 3.5 	imes 10^{-5} 	imes \frac{10^{-2}}{50 	imes 10^{-4}} = 3.5 	imes 10^{-5} 	imes \frac{1}{50} 	imes 10^2 = 0.07 	imes 10^{-4} = 7 	imes 10^{-6} \ \Omega$.

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