Question

Please help me. its a resistivity problem​

Answer 1

Answer

0.9375 metre or 93.75 centimetre

Explanation

Given, two wires made of iron and silver have same thickness. The length of iron wire = 15 cm = 0.15 m

To find the length of silver wire if both have same resistance.

We are given the resistivity of iron, say $\sf\rho_1$= 10 × 10^-8 ohm metre

And resistivity of silver, say $\sf\rho_2$ = 1.6 × 10^-8 ohm metre

We know that Resistance = $\sf \rho\frac{L}{A}$

Where rho is resistivity of material, L is length of wire and A is the area of cross section of wire.

Let the length of silver wire required be l. Since both wires have same thickness, let the area of cross section of both wires be A.

Equating the two resistances,

$\sf R_{iron} = R_{silver}$

$\sf\rho_1\frac{0.15}{A} = \rho_2\frac{l}{A}$

$\sf\implies l = \frac{\rho_1}{\rho_2}\times 0.15$

Put the values of resistivity

$\sf\implies l = \frac{10 × 10^{-8}}{1.6 × 10^{-8}} \times 0.15$

$\sf\implies l = \frac{1.5}{1.6}$

$\sf\implies l = 0.9375 m$