Question

A uniform rectangular segment of copper wire with length and cross-sectional area has resistance: R. Then this resistor is melted down, and 1/5 the material is used to make a new uniform rectangular resistor with resistance R. What is the length of thisnew resistor?

Answer 1

Step-by-step explanation:

Let L and A be the length and area of cross section of rectangular segment

If resistor is melted down to and its
`(1)/(5)` material is used to make a new uniform rectangular resistor with same resistance R

volume of original rectangular(V)
`=A* L`

Volume of new rectangular segment with length
`L_0(V_0)=A* L_0`

`5V_0=V`

`5* A_0* L_0=A* L`----1

Resistance is same

`R=(\rho L)/(A)=(\rho L_0)/(A_0)`

`(L)/(L_0)=(A)/(A_0)`

substitute
`(L)/(L_0)` in 1

`5=(L^2)/(L_0^2)`

`(L)/(L_0)=√(5)`

`L=√(5)L_0`

`L_0=(L)/(√(5))`