An aluminum wire consists of the three segments shown in FIGURE P27.64. The current in the top segment is 10 A. For each of these three segments, find the drift velocity v_d. Place your results in a table for easy viewing.

검증된 단계별 안내

Understand the problem: The drift velocity (v_d) of electrons in a conductor is given by the formula:

v

_d = InqA, where I is the current, n is the number density of conduction electrons, q is the charge of an electron, and A is the cross-sectional area of the wire. We need to calculate v_d for each segment of the aluminum wire using this formula.

Step 1: Identify the given values. The current (I) in the top segment is 10 A. For aluminum, the number density of conduction electrons (n) is approximately

2.5 × 10

²⁸ m^-3, and the charge of an electron (q) is

1.6 × 10

^-19 C. The cross-sectional area (A) for each segment will depend on the dimensions provided in the figure (e.g., diameter or radius).

Step 2: Calculate the cross-sectional area (A) for each segment. If the diameter (d) or radius (r) of the wire is given, use the formula for the area of a circle:

A = π r

². Ensure that the radius is in meters for consistency in SI units.

Step 3: Substitute the known values into the drift velocity formula for each segment. For example, for the top segment:

v

_d = 10(2.5 × 10²⁸)(1.6 × 10^-19)A. Repeat this calculation for the other two segments, using their respective cross-sectional areas.

Step 4: Organize the results into a table. For each segment, list the current (I), cross-sectional area (A), and calculated drift velocity (v_d). Ensure that the units are consistent and clearly labeled in the table.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Drift Velocity

Drift velocity is the average velocity that charged particles, such as electrons, attain due to an electric field. It is a crucial concept in understanding how current flows through a conductor. The drift velocity can be calculated using the formula v_d = I/(nAe), where I is the current, n is the charge carrier density, A is the cross-sectional area, and e is the charge of an electron.

Current

Current is the rate of flow of electric charge in a circuit, measured in amperes (A). In this context, the current in the aluminum wire segments affects the drift velocity of the electrons. Understanding how current relates to drift velocity is essential for calculating the drift velocity in each segment of the wire.

Conductivity and Resistivity

Conductivity is a measure of a material's ability to conduct electric current, while resistivity is its opposition to current flow. These properties are influenced by the material's composition and temperature. In the context of the aluminum wire, knowing the conductivity allows for the calculation of drift velocity, as it directly affects the relationship between current and electric field in the wire.