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  4. The specific resistance of a wire is p, its volume is 3m3 and its resistance is 3 Ω , then its length will be

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Q. The specific resistance of a wire is p, its volume is $ 3{{m}^{3}} $ and its resistance is 3 $ \Omega $ , then its length will be

CMC MedicalCMC Medical 2010

Solution:

Volume $ =Al=3 $ $ A=\frac{3}{l} $ Now, $ R=\rho \frac{l}{A} $ $ 3=\frac{\rho \times l}{3/l} $ $ {{l}^{2}}=\frac{9}{\rho } $ $ \Rightarrow $ $ l=\frac{3}{\sqrt{\rho }} $