Relation between Current and Drift Velocity
Derivation and application of the fundamental relationship between electric current (I) and drift velocity (vd): I = nAevd.
What is Relation between Current and Drift Velocity?
The average velocity attained by charge carriers (like electrons) in a conductor when an electric field is applied, causing them to move in a directed manner against their random thermal motion.
Key formula / rule: Relation between Current and Drift Velocity
Key points
- Understand the concept of drift velocity.
- Derive the relationship between current and drift velocity.
- Apply the formula I = nAevd to solve problems.
- Differentiate between drift velocity and signal propagation speed.
Common exam trap
Confusing drift velocity with the speed of electrical signals.
Definitions
- Term
Drift Velocity (vd)
- Meaning
The average velocity attained by charge carriers (like electrons) in a conductor when an electric field is applied, causing them to move in a directed manner against their random thermal motion.
- Term
Charge Carrier Density (n)
- Meaning
The number of free charge carriers (e.g., free electrons in a metal) per unit volume of the material.
Learning objectives
Understand the concept of drift velocity.
Derive the relationship between current and drift velocity.
Apply the formula I = nAevd to solve problems.
Differentiate between drift velocity and signal propagation speed.
Formulae
- Name
Relation between Current and Drift Velocity
- Note
I: Current, n: Number density of charge carriers, A: Cross-sectional area, e: Charge of a carrier, vd: Drift velocity.
- Expression
I = nAevd
- Name
Drift Velocity in terms of Electric Field
- Note
vd: Drift velocity, μ: Mobility of charge carriers, E: Electric field strength.
- Expression
vd = μE
Prerequisites
Electric Current and Ohm's Law
Electric Field and Potential
Charge Carriers in Conductors
Common mistakes
Confusing drift velocity with the speed of electrical signals.
Assuming drift velocity is constant; it depends on the electric field and material properties.
Incorrectly applying the formula I = nAevd, especially with units or sign conventions for charge.
Keywords
Drift Velocity
Electric Current
Charge Carriers
Conductivity
Mobility
nAevd
Practice preview
A wire of length L and cross-sectional area A has n free electrons per unit volume. If the drift velocity of electrons is v_d, the current flowing through the wire is proportional to:…
easy
In a wire, if the temperature increases, the drift velocity of electrons will:…
medium
If the number density of charge carriers in a conductor is 'n', the charge of each carrier is 'e', the cross-sectional area is 'A', and the drift velocity is 'v_d', what is the current flowing through the conductor?…
easy