Solve Conductor Questions: Find Total Current Carried by Silver Wire

[838]

Homework Statement

A 2.0-m length of silver wire has a uniform cross-sectional area of $$0.6mm^2$$. If the drift velocity in this wire is 5.0 x $$10^{-5}$$ m/s and the electrons all move in the same direction along the wire. What is the total current carried by the wire?

Homework Equations

So, silvers atomic mass is 107.9 g/mol and the density is 10500 $$kg/m^2$$.
Also, conductivity of silver is 6.3 x $$10^7$$ (too lazy to add units)

So, I = JA, I have A, so I'll find J.
J=nq$$V_d$$
where n = number density of atoms
q is charge constant (1.6 x $$10^{-19}$$)
and $$V_d$$ is the drift velocity.

The Attempt at a Solution

So, I think I have an answer, my instructor said it was wrong, but wouldn't tell me until after the homework is due (no free points, I guess it's fair).

n=10500/$$m^3$$*(1mol/0.1079kg)*(6.02 x $$10^{23}$$/1mol) = 5.85 x $$10^{28}$$

J=nq$$V_d$$

(5.85 x $$10^{28}$$)*(1.6 x $$10^{-19}$$)*(5.0 x $$10^{-5}$$)
= 468656.16

Area = $$0.6mm^2$$ = 0.6 x$$10^{-6}$$m

Now, to find I. I=(468656.16 N/C)*(0.6 x$$10^{-6}$$m) = 0.28Amps.

Does this look correct? Sorry if my work is a little sloppy.

 

[anathema]

Your solution looks correct to me. The only thing I would suggest is to be careful with your units. For the number density, you have converted from kg to m^3, but you still have kg in your final answer. You may want to double check your units throughout your calculations to make sure they are consistent.

Also, it may be helpful to label your final answer with the correct units (Amps) to make it clear to the reader.

Overall, your approach and solution seem sound. If your instructor has a different answer, it would be helpful to understand where the discrepancy lies. Perhaps there is a different value for the conductivity of silver or a different value for the drift velocity that your instructor is using.

I hope this helps! Keep up the good work.

 

[Moetasim]

Your approach to solving this problem is correct. However, your final answer of 0.28 amps is incorrect. The correct answer is 2.81 x 10^-4 amps. This may be where your instructor found an error. Make sure to double check your calculations and units. Good job on using the correct equations and applying them correctly to solve the problem. Keep up the good work!