# What must be the length of this wire? What must be the diameter of this wire?

Suppose you wish to fabricate a uniform wire from 1.80 g of copper. The wire is to have a resistance of

R = 0.520 Ω

and all the copper is to be used.

(a) What must be the length of this wire?
m

(b) What must be the diameter of this wire?
µm
asked Feb 2, 2012 in Physics

Copper is a good conductor because its resistivity is low. We expect to find that this wire is very long and thin.

To solve for the variables, we will use the equation for resistance as a function of resistivity, length, and cross-sectional area.

A = m / (l*p)    (*where A=area, m=mass, l=length, p=density)

R = l / (r*A)  (*where R=resistance, l=length, r=resistivity, A=area)

Now substitute A into equation for R.

R = l / (r*m / (l*p)) = (r*p*l2) / m

Now solve for L:

l = squareroot(m*R/r*p)

where m = 1.8×10-3 kg

R = 0.52 Ω

r = 1.70 × 10−8 Ω · m

p = 8.92 × 103 kg/m3

Plug in values and solve for l:

l = squareroot((1.8×10-3 kg * 0.52 Ω) / (1.70 × 10−8 Ω · m r * 8.92 × 103 kg/m3 ))

l = 2.48m

Part B, the diameter can be found by noting that:

A = pi*r^2   (*r=radius, and r=d/2  d=diameter)

A=pi(d/2)^2  = m/(l*p)

solving for d:

d = squareroot (4*m/(pi*l*p))

plugging in the values we get that d:

d = squareroot (4*1.8×10-3 kg / (pi*2.48m * 8.92 × 103 kg/m3))

d = 3.219*10^-4 = 3.21 µm

answered Feb 2, 2012 by ~Expert~ (3,020 points)
selected Feb 2, 2012 by yoshi