What Is the Diameter of a Tungsten Filament with a Given Length and Resistance?

[rinarez7]

1. A 1.3 cm length of tungsten filament in a small lightbulb has a resistance of 0.032 ohms. Find its diameter.
Given: Length= 1.3 cm= .013m
R= 0.032 ohms
resistivity= 5.6e-8 ohms*meter



2.
A= pi (r^2)
R= resistivity (Length/ Area)

The Attempt at a Solution

R= resistivity ( Length/ pi* (r^2) )
.032 ohms= (5.6e-8 ohms*meter) * (.o13m/ (pi* (r^2)) )
.032 (pi) (r^2) = 7.28e-10
.100530965 (r^2) = 7.28e-10
r= 8.509e-5
diameter= 2r= 1.701e-4m

It asks for the answer in mm, so I divided my answer by 1000= 1.7 e-7 mm, but it's not correct = (
What am I missing?
Thanks in advance!

 

[mgb_phys]

Try multplying your answer by a 1000?
If you have an answer in m, the answer in mm is going to a be BIGGER number

 

[Netspin]

What makes Physics physical are the units. Units are as essential to the solution procedure as the mathematical expressions used to determine its quantities. Therefore, units must accompany their magnitudes throughout. In fact, this will often help as a conincident double check on the answer. Tables of Fundamental Units can be found in many books.
In your problem to convert your answer, already in meters, into millimeters, you recall that multiplying by one (1) doesn't change much.
Since 1 meter = 1,000 millimeters, you could divide one side by the other to arrive at the same answer: 1. In order to have millimeters appear in your answer then, you would multiply your answer in meters by 1,000 millimeters/1 meter (i.e. 1). As you can see the meters cancel out leaving the units in millimeters.
You could multiply it by 1 meter/1,000 millimeters also 1, but then you have to consider you've expressed the diameter, a linear measurement in terms of
10 e-3 meters^2/millimeters an unorthodox form but frankly not incorrect.

 

[Netspin]

Of course that "1,000" factor has to multiply your numerical answer since you have just multiplied your meters by "milli".