If a current-carrying wire has a cross-sectional area that...

If a current-carrying wire has a cross-sectional area that gradually becomes smaller along the length of the wire, the drift velocity A. increases along the length of the wire. B. decreases along the length of the wire. C. remains the same along the length of the wire. D. increases along the length of the wire only if the resistivity increases too. E. decreases along the length of the wire only if the resistivity decreases too.

If a current-carrying wire has a cross-sectional area that gradually becomes smaller along the length of the wire, the drift velocity
A. increases along the length of the wire.
B. decreases along the length of the wire.
C. remains the same along the length of the wire.
D. increases along the length of the wire only if the resistivity increases too.
E. decreases along the length of the wire only if the resistivity decreases too.

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Key Concepts

Drift Velocity

Drift velocity is the average velocity attained by charged particles, such as electrons, due to the influence of an electric field in a conductor. It is directly proportional to the current and inversely proportional to the cross-sectional area when the number of charge carriers is constant.

Current Continuity

Current continuity implies that in a steady-state current flow, the amount of charge passing through any cross-section of the conductor remains constant. This means that if the cross-sectional area of the wire changes, the drift velocity of the charge carriers must adjust to maintain the same current.

Relationship between Current, Drift Velocity, and Cross-Sectional Area

This relationship is described by the equation I = n e A v_d, where I is the current, n is the charge carrier density, e is the charge of each carrier, A is the wire's cross-sectional area, and v_d is the drift velocity. Given a constant current and charge carrier density, a decrease in area leads to an increase in drift velocity.

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