Electrical Resistivity Equation

[Matt.D]

Is the correct equation that relates to the electrical resistivity of a conducting material to its resistance:

p = RS/l

p = is the electrical resistivity
R = is the resistance of the material
S = is the cross-sectional area
l = is the length of the specimen

if I'm using the right formula, would my answer to this question be correct?

A potential difference of 1.5V exists across the ends of a copper wire of length 2.0m and uniform radius 0.40mm. Calculate the current in the wire.

I've been given the resistivity of copper as 1.7 x 10^-4 ohms.meter

[Answer]

p = RS/l
= (1.7 x 10^-4) x 0.40mm / 2.0m
= 0.0007 x 0.0004 / 2.0
= 0.00000014

corecto?

 

[Doc Al]

Is the correct equation that relates to the electrical resistivity of a conducting material to its resistance:

p = RS/l

p = is the electrical resistivity
R = is the resistance of the material
S = is the cross-sectional area
l = is the length of the specimen

That's correct.

if I'm using the right formula, would my answer to this question be correct?

Only if you use it correctly!

p = RS/l
= (1.7 x 10^-4) x 0.40mm / 2.0m
= 0.0007 x 0.0004 / 2.0
= 0.00000014

Not correct. (If you checked the units of your calculation, you'd see that things don't match.)

First, you need to calculate the resistance (R) of that piece of copper wire, not the resistivity ($\rho$, which is a fixed property of copper). You are given the resistivity, not the resistance. Rearrange that formula as so:
$$R = \rho L / S$$
Once you find the resistance, then you can use Ohm's law to find the current.

 

[Matt.D]

Thanks Doc!

Using the rearranged formula I've calculated:

R = pl/S

R = 0.0007 x 2.0 / 0.0004

R = 0.0014 / 0.0004

R = 3.5 Ohms

Using Ohms Law

I = V/R

I = 1.5V (as stated in the question) / 3.5 ohms

I = 0.42857..

I = 0.43

 

[Gokul43201]

You are given the radius of the wire, not its cross-sectional area.

 

[Matt.D]

Thanks Gokul! I've really got to start reading questions more thoroughly.. I'm losing marks like this all of the time