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

Step-by-step 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=(\rho L)/(A)`

Where R=resistance

`\rho =resistivity`

L=Length

A=area of cross-section

`A=(\pi d^2)/(4)`

Thus
`R\propto (L)/(d^2)`

therefore

`R_1\propto (L_1)/(d_1^2)`--------1

`R_2\propto (L_2)/(d_2^2)`--------2

divide 1 and 2 we get

`(R_1)/(R_2)=(L_1)/(L_2)* (d_2^2)/(d_1^2)`

`(R_1)/(R_2)=(30)/(40)* (3.5^2)/(3^2)`

`R_2=25* 0.734* 1.33`

`R_2=24.47 \Omega`