Question

UNITS OF RESISTIVITY - Calculate the resistance of 100cm length of wire having a uniform cross-sectional area of 0.1mm^2 if the wire is made of manganin having a resistivity of 50x10^8 ohms-m. if the wire is drawn out to three times its original length, by how many times would you expect its resistance to be increased? Ans(500ohms; 9 times) Need solution, please help...

Answer 1

\[R=\frac{\ell\rho}{A}\]

Answer 2

When the wire is drawn out to three time its original length the volume remains constant
\[V=A\ell=A_2\ell_2\]
\[\ell_2=3\ell\]\[A_2=\frac {A}3\]

Answer 3

\[R_2=\frac{\ell_2\rho}{A_2}=\frac{3\ell\rho}{A/3}=9\frac{\ell\rho}{A}=9R\]

Answer 4

But I think you have got the wrong value for the resistivity of manganin
\[\rho_{\text{manganin} }\approx50\times 10^{-8}[\Omega\text{ m}]\]

Answer 5

\[\ell=100[\text{cm}]=1[\text m]\]\[A=0.1[\text{mm}^2]=1\times10^{-7}[\text m^2]\]\[\rho=5\times10^{-7} [\Omega\text{ m}]\]

Answer 6

\[R=\frac{\ell\rho}{A}=\frac{1[\text m]\times5\times10^{-7}[\Omega\text{ m}]}{1\times10^{-7}[\text m^2]}=5[\Omega]\]
\[R_2=\frac{\ell_2\rho}{A_2}=\frac{3\times1[\text m]\times5\times10^{-7}[\Omega\text{ m}]}{1/3\times10^{-7}[\text m^2]}=9\times5[\Omega]\]

Answer 7

im not sure how they got 500Ω

maybe i made a mistake somewhere