Two wires of different materials, resistivity of the first is half that of the second, length of the first is three times the second and its density is double that of the second. Find the ratio between their resistances.
The resistance \(R\) of a object of resistivity \(\rho\), length \(\ell\), and cross-section \(A\) is: \[R=\rho\frac{\ell}{A}\]
\(\rho_1 = \rho_2/2\), \(\ell_1 = 3\ell_2\), \(\varrho _1 =2\varrho_2\) where \(\varrho\) is density
Which kind of density is referred to in the question; mass density, current density, charge density?
How do the cross sectional areas of the wires compare, or do we just assume they are the same ? I'm wondering why the density is mentioned, is there more to this question that you haven't posted ?
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