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The electron drift speed in metals is sm...

The electron drift speed in metals is small `(~ ms^(-1))` and the charge of the electron is also very small `(~ 10^(-19)C)`, but we can still obtain a large amount of current in a metal. Why?

A

Conducting property of the conductor

B

Resistance of the conductor is small

C

Electron number density of the conductor is small

D

Electron number density of the conductor is enomous

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To understand why we can obtain a large amount of current in a metal despite the small drift speed of electrons and their small charge, we can break down the explanation step by step: ### Step 1: Understanding Current Current (I) in a conductor is defined as the rate of flow of charge. The formula for current can be expressed as: \[ I = n \cdot e \cdot v_d \cdot A \] where: - \( I \) = current - \( n \) = electron density (number of charge carriers per unit volume) - \( e \) = charge of an electron (approximately \( 1.6 \times 10^{-19} \, C \)) - \( v_d \) = drift velocity of electrons - \( A \) = cross-sectional area of the conductor ### Step 2: Analyzing the Factors In this formula, while both the charge of the electron \( e \) and the drift velocity \( v_d \) are small, the current can still be large if the electron density \( n \) is sufficiently high. ### Step 3: Electron Density in Metals Metals have a very high electron density. This means that there are a large number of free electrons available to carry charge. For example, in metals like copper, the electron density can be on the order of \( 10^{28} \, m^{-3} \). ### Step 4: Contribution of Electron Density Since the electron density \( n \) is very large in metals, even though \( e \) and \( v_d \) are small, the product \( n \cdot e \cdot v_d \) can result in a significant current. The high number of charge carriers compensates for their low individual contributions. ### Step 5: Conclusion Thus, the large amount of current in a metal can be attributed primarily to the high electron density, which allows for a substantial flow of charge despite the small drift speed and small charge of individual electrons. ### Final Answer The reason we can obtain a large amount of current in a metal, despite the small drift speed and small charge of electrons, is due to the enormous electron density in metals. ---
To understand why we can obtain a large amount of current in a metal despite the small drift speed of electrons and their small charge, we can break down the explanation step by step: ### Step 1: Understanding Current Current (I) in a conductor is defined as the rate of flow of charge. The formula for current can be expressed as: \[ I = n \cdot e \cdot v_d \cdot A \] where: - \( I \) = current - \( n \) = electron density (number of charge carriers per unit volume) ...
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