Question

the electrical resistance of copper wire varies directly with its length and inversely with the square of the diameter of the wire. If a wire 30m long with a diameter of 3 mm has a resistance of 25 ohms, find the resistance of a wire 40m long with a diameter of 3.5 mm

Answer 1

Answer:24.47

Explanation:

Given

$L_1=30 m$

$d_1=3 mm$

$R_1=25 \Omega$

$L_2=40 m$

$d_2=3.5 mm$

we know Resistance $R=\frac{\rho L}{A}$

Where R=resistance

$\rho =resistivity$

L=Length

A=area of cross-section

$A=\frac{\pi d^2}{4}$

Thus $R\propto \frac{L}{d^2}$

therefore

$R_1\propto \frac{L_1}{d_1^2}$--------1

$R_2\propto \frac{L_2}{d_2^2}$--------2

divide 1 and 2 we get

$\frac{R_1}{R_2}=\frac{L_1}{L_2}\times \frac{d_2^2}{d_1^2}$

$\frac{R_1}{R_2}=\frac{30}{40}\times \frac{3.5^2}{3^2}$

$R_2=25\times 0.734\times 1.33$

$R_2=24.47 \Omega$