CBSE Class 10 Answered
the resistance of a wire of 0.01 cm radius is 10 ohm.if the resistivity of the material of the wire is 50*10^-8 ohm meter find the length of the wire
Asked by prassanna.j | 03 Sep, 2023, 12:28: PM
Resistance R of wire of length L is ![begin mathsize 14px style R space equals space rho cross times L over A end style](https://images.topperlearning.com/topper/tinymce/cache/fc92b13536a3da022b12a5494b58e0ba.png)
![begin mathsize 14px style R space equals space rho cross times L over A end style](https://images.topperlearning.com/topper/tinymce/cache/fc92b13536a3da022b12a5494b58e0ba.png)
Where ρ is resistivity of material of wire and A is area of cross section .
If r is rhe radius of cross section of wire , then resistance R is ![begin mathsize 14px style R space equals space rho cross times fraction numerator L over denominator pi space r squared end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/bf7d21e4cbaefc610c463f26f09849da.png)
![begin mathsize 14px style R space equals space rho cross times fraction numerator L over denominator pi space r squared end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/bf7d21e4cbaefc610c463f26f09849da.png)
Hence of length L of wire is
![begin mathsize 14px style L space equals space R space cross times space left parenthesis space straight pi space straight r squared space right parenthesis space divided by space straight rho end style](https://images.topperlearning.com/topper/tinymce/cache/120bc447dbe1c921594791f6b168cd1f.png)
![begin mathsize 14px style L space equals space fraction numerator 10 space cross times space left parenthesis pi space cross times space left parenthesis 0.01 space cross times space 10 to the power of negative 2 end exponent right parenthesis to the power of 2 space end exponent right parenthesis space over denominator left parenthesis space 50 space cross times space 10 to the power of negative 8 end exponent right parenthesis end fraction space m space equals space 0.628 space space m end style](https://images.topperlearning.com/topper/tinymce/cache/2a3512732ce7038f4dca4bcbdca832b3.png)
Answered by Thiyagarajan K | 03 Sep, 2023, 15:59: PM
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