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

Answer:

So after stretching new resistance will be 0.1823 ohm

Explanation:

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

Radius of the wire $r_1=0.32mm=0.32\times 10^{-3}m$

Resistance of the wire initially $R_1=90ohm$

We know that resistance is equal to $R=\frac{\rho l}{A}$ ,here $\rho$ is resistivity, l is length and A is area

From the relation we can say that $\frac{R_1}{R_2}=\frac{l_1}{l_2}\times \frac{A_2}{A_1}$

Now length of wire become 6.75 m

Volume will be constant

So $A_1l_1=A_2l_2$

So $\pi \times (0.32)^2\times150=\pi \times r_2^2\times 6.75$

$r_2=1.508mm$

So $\frac{90}{R_2}=\frac{150}{6.75}\times \frac{1.508^2}{0.32^2}$

$R_2=0.1823ohm$