Relation between Electric Current and Drift Velocity
The electric current (I) flowing through a conductor is directly related to the drift velocity (vd) of charge carriers by the formula I = nAevd, where n is charge carrier density, A is cross-sectional area, and e is elementary charge.
What is Relation between Electric Current and Drift Velocity?
The rate at which electric charge flows through a conductor. It is measured in Amperes (A).
Key formula / rule: Current and Drift Velocity
Key points
- To understand the concept of drift velocity.
- To derive the relationship between electric current and drift velocity.
- To apply the formula I = nAevd in problem-solving.
- To appreciate the microscopic origin of electric current.
Common exam trap
Confusing drift velocity with the random thermal velocity of charge carriers.
Definitions
- Term
Electric Current (I)
- Meaning
The rate at which electric charge flows through a conductor. It is measured in Amperes (A).
- Term
Drift Velocity (vd)
- Meaning
The average velocity attained by charge carriers (like electrons) in a material due to an applied electric field. It is typically very small.
- Term
Charge Carrier Density (n)
- Meaning
The number of charge carriers per unit volume of the material.
Learning objectives
To understand the concept of drift velocity.
To derive the relationship between electric current and drift velocity.
To apply the formula I = nAevd in problem-solving.
To appreciate the microscopic origin of electric current.
Formulae
- Name
Current and Drift Velocity
- Note
I is electric current, n is the number density of charge carriers, A is the cross-sectional area of the conductor, e is the magnitude of the charge of each carrier, and vd is the drift velocity.
- Expression
I = nAevd
- Name
Drift Velocity in terms of Electric Field
- Note
Where E is the electric field, τ is the average time between collisions (relaxation time), and m is the mass of the charge carrier. This formula is related but not directly the primary focus of I=nAevd.
- Expression
vd = (eEτ)/m
Prerequisites
Concept of electric charge and its properties.
Understanding of electric field and potential difference.
Definition of electric current.
Basic understanding of conductors and charge carriers.
Common mistakes
Confusing drift velocity with the random thermal velocity of charge carriers.
Incorrectly assuming that drift velocity is very high; it is typically very small (of the order of mm/s).
Forgetting to include the charge carrier density (n) or the cross-sectional area (A) in calculations.
Using the wrong sign for charge carriers (e.g., using positive charge for electrons in the formula if not careful about direction).
Keywords
Electric Current
Drift Velocity
Charge Carriers
Conductor
Number Density
Cross-sectional Area
Elementary Charge
Practice preview
What is the relationship between electric current (I) and drift velocity (v_d) in a conductor?…
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If the drift velocity of electrons in a conductor is doubled, what happens to the electric current, assuming other factors remain constant?…
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Consider a metallic wire of length L and cross-sectional area A. If a potential difference V is applied across its ends, resulting in an electric field E and drift velocity v_d for electrons (charge e, mass m), which of …
hard