Question

If two different wires having identical cross-sectional areas carry the same current, will the drift velocity be higher or lower in the better conductor? Explain in terms of the equation vd=InqA, by considering how the density of charge carriers n relates to whether or not a material is a good conductor.

a) Higher in the better conductor, as more charge carriers lead to higher drift velocity.

b) Lower in the better conductor, as fewer charge carriers lead to higher drift velocity.

c) The drift velocity is independent of the material's conductivity.

d) Drift velocity is not related to charge carriers.

Answer 1

In a better conductor, the drift velocity will be lower because the charge carrier density is higher, meaning more carriers are available to transport the same current, reducing the need for each carrier to move quickly.

Step-by-step explanation:

When comparing drift velocity in different conductors carrying the same current, it's essential to understand the relationship expressed by the equation I = nqAvd. Here, I represents the current, n is the charge carrier density, q is the charge of each carrier, A is the cross-sectional area of the wire, and vd is the drift velocity. Since the current and the cross-sectional area are constant in our case, the drift velocity is inversely proportional to the charge carrier density. A conductor with a higher density of charge carriers, typical of a better conductor, will therefore have a lower drift velocity because there are more charge carriers to carry the same amount of current, which means each charge carrier needs to move less swiftly.

If the current density in the wire increases, the drift velocity of the charges also increases because current density is directly proportional to the current and inversely proportional to the area.