Question

A metal wire 1.50 m long has a circular cross section of radius 0.32 mm and an end-to-end resistance of 90.0 Ohms. The metal wire is then stretched uniformly so that its cross-section is still circular but its total length is now 6.75 m. What is the resistance of the wire after stretching? (Units: Ohm.)

Answer 1

So after stretching new resistance will be 0.1823 ohm

Step-by-step explanation:

We have given initially length of the wire
`l_1=150m`

Radius of the wire
`r_1=0.32mm=0.32* 10^(-3)m`

Resistance of the wire initially
`R_1=90ohm`

We know that resistance is equal to
`R=(\rho l)/(A)` ,here
`\rho` is resistivity, l is length and A is area

From the relation we can say that
`(R_1)/(R_2)=(l_1)/(l_2)* (A_2)/(A_1)`

Now length of wire become 6.75 m

Volume will be constant

So
`A_1l_1=A_2l_2`

So
`\pi * (0.32)^2*150=\pi * r_2^2* 6.75`

`r_2=1.508mm`

So
`(90)/(R_2)=(150)/(6.75)* (1.508^2)/(0.32^2)`

`R_2=0.1823ohm`