Question

A tightly coiled spring has 75 coils, each 3.50 cm in diameter. the coil is made of insulated metal wire that is 3.25 mm in diameter. An ohmmeter connected across opposite ends of the spring measures a resistance of 1.74. What is the resistivity of the metal?
A. 7.50 x 10^-3 * m
B. 3.25 x 10^-3 * m
C. 1.75 x 10^-6 * m
D. 8.30 x 10^-6 * m

Answer 1

Answer:

Correct option: C

Explanation:

Resistance and Resistivity

The resistance of a conductor with cross-section area A, length L and resistivity \rho is given by

$\displaystyle R=\frac{\rho L}{A}$

If we know the value of R, then we can solve for $\rho$ as follows

$\displaystyle \rho=\frac{AR}{L}$

The coiled spring has n=75 coils with a diameter of d=3.5 cm = 0.035 m. This will be used to compute the total length of the conductor. The length of a circle of diameter d is:

$L_c=\pi d$

For 75 turns, the total length is  

$L=75\pi d=75\pi \times 0.035$

$L=8.25\ m$

The cross-section area is computed as the area of a circle

$\displaystyle A=\frac{\pi d_c^2}{4}$

The diameter of the conductor is dc = 3.25 mm = 0.00325 m

$\displaystyle A=\frac{\pi 0.00325^2}{4}$

$A=8.30\times 10^{-6}\ m^2$

We now compute the resistivity

$\displaystyle \rho=\frac{8.30\times 10^{-6}\ m^2\times 1.74\ \Omega }{8.25\ m}$

$\boxed{\rho=1.75\times 10^{-6}\ \Omega .m}$

Correct option: C