Verified Solution • 2025–26 Session moderate

QPages 198-203: Q6: HC Verma: Concepts of Physics - Volume 2 Electric Current in Conductors Pages 198-203: Q6 Solution: A wire of length 1 m and radius 0.1 mm has a resistance of .…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often plug the radius in millimetres directly into $A=\pi r^2$, forgetting to convert $0.1\,\text{mm}$ to $1\times10^{-4}\,\text{m}$; this squares the error and yields a resistivity off by a factor of $10^6$. Always convert length units to metres before squaring and use the radius (not the diameter) in the area formula.

A wire of length 1 m and radius 0.1 mm has a resistance of 100 Ω100 \ \Omega. Find the resistivity of the material.

Step-by-Step Verified Solution

**Answer:** rho=3.14times10−6Omegatextm\\rho = 3.14 \\times 10^{-6}\\ \\Omega\\text{m}. **Step-by-Step Explanation:** Given: l=1l = 1 m, r=0.1r = 0.1 mm =10−4= 10^{-4} m, R=100OmegaR = 100\\ \\Omega. A=pir2=3.14times10−8A = \\pi r^2 = 3.14 \\times 10^{-8} m_. rho=fracRAl=100times3.14times10−8=3.14times10−6Omegatextm\\rho = \\frac{RA}{l} = 100 \\times 3.14 \\times 10^{-8} = 3.14 \\times 10^{-6}\\ \\Omega\\text{m} [citation:6][citation:9].

All Questions in this Chapter

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