Question

The electrical resistance (R) of a wire at any given temperature varies directly to the length (L). At a certain temperature, a 100-meters long wire has a resistance of 12.5 ohms. In the same condition, what is the electrical resistance of a wire 250meters long?​

Answer 1

Answer:

$R = 31.5 \: \Omega$

Step-by-step explanation:

We have been given that the Resistance of a 100 m long wire at a certain temperature is 12.5 $\Omega$

The relation for Resistance of a wire is given by:-

$R=\dfrac{\rho\times L}{A}$

Here:-

$12.5 = \dfrac{\rho\times 100}{A} \\ \\ \\\\\dfrac{\rho}{A} = \dfrac{12.5}{100}$


This relation holds true at a certain temperature.

Resistance is directly proportional to the length of the wire. If the length is changed then the resistance changes as well.

Resistance in a 250 metres long wire will be:-

$R = \dfrac{\rho \times 250}{A}$

$R = \dfrac{12.5}{100} \times 250 \\ \\ \\R = 31.5 \: \Omega$