Question

The resistance, R of a wire varies directly as the length, l, and inversely as the diameter, d, squared. If R is 1.50ohms when l=2.0 m and d=1.5 mm, what is the resistance of a wire made of the same material that is 8.0 m long and has a diameter of 3.0 mm?

Answer 1

resistance is 1.5 ohms (1.5 Ω)

Explanation:

R varies directly with l

R varies inversely with
`d^2`

We can set-up a proportionality statement as shown below:

`R=k(l)/(d^2)`

Now, Given,

R = 1.50

l = 2

d = 1.5

We substitute and find k (the proportionality constant):

`R=k(l)/(d^2)\\1.5=k(2)/(1.5^2)\\1.5=(2k)/(2.25)\\2k=1.5*2.25\\2k=3.375\\k=1.6875`

Now, we will use this value of k to solve the problem.

Given,

l = 8

d = 3

and

k = 1.6875

We find R:

`R=k(l)/(d^2)\\R=1.6875(8)/(3^2)\\R=(1.6875*8)/(9)\\R=1.5`

The resistance is 1.5 ohms (1.5 Ω)