A rod of a certain metal is $1.0\, m$ long and $0.6\, cm$ in diameter. Its resistance is $3.0 × {10^{ - 3}}\, ohm$. Another disc made of the same metal is $2.0\, cm$ in diameter and $1.0\, mm$ thick. What is the resistance between the round faces of the disc
Diffcult
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(b) Resistivity of the material of the rod $\rho = \frac{{RA}}{l} = \frac{{3 \times {{10}^{ - 3}}\pi {{(0.3 \times {{10}^{ - 2}})}^2}}}{1}$= $27 \times {10^{ - 9}}\pi \,\Omega \times m$
Resistance of disc $R = \frac{{({\rm{Thickness}})}}{{({\rm{Area\, of \,cross }}\,{\rm{section}})}}$
= $27 \times {10^{ - 9}}\pi \times \frac{{({{10}^{ - 3}})}}{{\pi \times {{(1 \times {{10}^{ - 2}})}^2}}}$$ = 2.7 \times {10^{ - 7}}\,\Omega .$
Resistance of disc $R = \frac{{({\rm{Thickness}})}}{{({\rm{Area\, of \,cross }}\,{\rm{section}})}}$
= $27 \times {10^{ - 9}}\pi \times \frac{{({{10}^{ - 3}})}}{{\pi \times {{(1 \times {{10}^{ - 2}})}^2}}}$$ = 2.7 \times {10^{ - 7}}\,\Omega .$
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