Question

there are two metalic wires of the name thickness made from iron and silver if the lenght of iron wire is 12 cm what should be lenght of silver while in equal to the resistance of iron wire​

Answer 1

ANSWER:

The length of silver wire is 73.2 cm.

EXPLANATION:

   The resistance of an object is directly proportional to the length of the object and inversely proportional to the "cross sectional area" of the object. The "cross sectional area" is directly proportional to thickness in case of wire being the object. So as the thickness of both the wires are same, the cross sectional area of both the wires will also be same.

  The constant of proportionality between the resistance of an object and length and area of that object is termed as resistivity or specific resistance. The specific resistance varies depending upon the nature of the object. Each element in the periodic table has their constant specific resistance value.  

In the present case, the iron and silver wires have same thickness which means their cross sectional area are equal and also the resistance of the both the wires are equal. So only the "length and specific resistance" of the wires will vary. The "formula for" calculating resistance is

$R=\frac{\rho L}{A}$

Here, ρ is the specific resistance, L is the length and A is the cross sectional area of the objects having resistance R.

In the present case, let us consider $\mathrm{R}_{\mathrm{I}} \text { and } \mathrm{R}_{\mathrm{s}}$ ­as the resistance of iron and silver wire respectively. Similarly,          are the specific resistance, $\mathrm{L}_{\mathrm{I}} \text { and } \mathrm{L}_{\mathrm{s}}$ are the lengths and $\mathrm{A}_{\mathrm{I}} \text { and } \mathrm{A}_{\mathrm{s}}$ are the "cross sectional areas" for iron and silver wire, respectively. Since the thickness and resistance of both the wires are same, so RI =Rs and AI = AS, thus

$\frac{R_{I}}{R_{S}}=\left(\frac{\rho_{I} L_{I}}{A_{I}}\right) *\left(\frac{A_{S}}{\rho_{S} L_{S}}\right)$

$1=\frac{\rho_{I} L_{I}}{\rho_{S} L_{S}}$

$\rho_{S} L_{S}=\rho_{I} L_{I}$

$\frac{\rho_{S}}{\rho_{L}}=\frac{L_{I}}{L_{S}}$

The specific resistance of silver and iron are 1.59 * 10-8 Ωm and 9.7*10-8 Ωm, respectively.

Thus,

$\frac{1.59 * 10^{-8}}{9.7 * 10^{-8}}=\frac{12}{L_{S}}$

$L_{S}=\frac{12}{1.59} * 9.7=73.2 \mathrm{cm}$

Thus the length of silver wire is 73.2 cm.