Given
Resistivity (ρ) = 1.7 × 10-8 Ωm
Diameter (d) = 0.1 mm = 0.1×10-3 m
(∵ 1m = 1000 mm)
Resistance (R) = 34 Ω
Area of cross section (A) = \(\frac{πd^2}{4}\)
A = \(\frac{3.14\,\times\,(0.1\,\times10^{-2})^2}{4}\)
Now,
R = ρ\(\frac{l}{A}\)
⇒ 34 = \(\frac{1.7\,\times\,10^{-8}\times1}{\frac{3.14\times(0.1\,\times10^{-2})^2}{4}}\)
⇒ \(\frac{34}{1.7\,\times\,10^{-8}}\,\times\,\frac{0.0314\,\times10^{-6}}{4}= l\)
⇒ l = \(\frac{17}{1.7\,\times\,10^{-8}}\,\times\,\frac{31.4\,\times10^{-9}}{2}\)
⇒ l = \(\frac{31.4}{2}\) = 15.7
Hence the length of the wire is 15.7 m.
