Question

A 13.5 Ω resistor is made from a coil of copper wire whose total mass is 14.0 g .

What is the diameter of the wire?

How long is the wire?

Answer 1

Given:

R = 3.5 ohm

M = 14 g = 14 x 10^-3 kg

Note that the resistivity of copper wire is approximately to

ohm-cm

And the density of the copper wire is

Den = 8.94 g/cm³ .

Hence

Den = Mass / Volume

Volume = Mass / Density

Volume = 14 / 8.94

Volume = 1.565 cm³

In simple way, we can say that

Volume = Area x length

V = AL

A = V/L

As we also know that the resistance of the wire is given by:

Putting the value of A in the equation, we get

L² = (R x Volume) ÷ (Rho)

L² = (13.5 x 1.56 ) ÷ (1.68 x 10^-6)

L = 3547.37 cm

L = 3.547 m

using again

A = Volume / Length

3.1415 x r² = 1.565/3547.37

r = 0.01183 cm

Diameter is equal to

D = 2 x 0.01183

D = 0.0236 cm