Question

A potential difference of 3.00 nV is set up across a 2.00 cm length of copper wire that has a radius of 2.00 mm. How much charge drifts through a cross section in 3.00 ms? The resistivity of copper is 8 rho 1.69 10 m − = ⋅ Ω⋅ .

Answer 1

3.35×10^-7C

Step-by-step explanation:

First we must put down the formula for charge drifting at a time t. But current is related to voltage by ohm's law as shown in the image attached. From the relation of ohm's law and the formula for resistivity, the expression that can be used to obtain the charge flowing at a time t, can be derived. Substitution of values gives the answer.

Answer 2

Answer: 0.335 μC

Step-by-step explanation:

The charge across the wire can be gotten by

Q = IT, where I is the current, and T is the time. Ω

Also, I = V/R, where V is the potential difference across the wire and R is the resistance of the wire.

R is also given as ρL/A, where A is πr²

Now, if we insert each of these formula in each other, we have

I = V/ [ρL/πr²]

I = V*π*r²/ρL

Q = V*π*r²*t / ρL so that

Q = [3*10^-9 * π * 0.002² * 3*10^-3] / [1.69*10^-8 * 0.02]

Q = [ 1.13*10^-16 ] / 3.38*10^-10

Q = 3.35*10^-7C

Q = 0.335 μC