---
title: "Current from drift velocity"
subject: "Basic Electrical Engineering"
chapter: 1
key: "semester_1/basic_electrical_engineering:drift-velocity-free-electron-current"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/drift-velocity-free-electron-current
site: BCT Engineering
---

# Current from drift velocity

Basic Electrical Engineering · Chapter 1: General Electric System

- Asked in: 2070 Asar, 6 marks
- Video: [Current from drift velocity (I = neAvd) | Electricity | Physics | Khan Academy](https://www.youtube.com/watch?v=-0Twobe3T18) — Khan Academy India - English
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_engineering/drift-velocity-free-electron-current
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_engineering/chapter-1

## Question

A conductor material has a free electron density of 10^24 electrons per m³. When a voltage is applied a constant drift velocity of 1.5×10⁻² m/s is attained by the electrons. If the cross sectional area of the material is 1 cm², calculate the magnitude of the current.

## Short answer

Current I = n e v_d A = 10^24 × 1.6×10^−19 × 1.5×10^−2 × 10^−4 = 0.24 A.

## Answer

Current in a conductor is the charge crossing a section per second: I = n e v_d A.

#### Data
- n = 10²⁴ electrons/m³
- e = 1.6 × 10⁻¹⁹ C
- v_d = 1.5 × 10⁻² m/s
- A = 1 cm² = 10⁻⁴ m²

#### Calculation
I = n e v_d A
I = 10²⁴ × 1.6 × 10⁻¹⁹ × 1.5 × 10⁻² × 10⁻⁴
I = 1.6 × 10⁵ × 1.5 × 10⁻² × 10⁻⁴
I = 2400 × 10⁻⁴ = 0.24 A

**Answer: I ≈ 0.24 A (240 mA)**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which formula gives the current from electron density, drift velocity and area?
   A. I = n e v_d A
   B. I = n e A / v_d
   C. I = n v_d / (e A)
   D. I = e v_d / (n A)
   Answer: A. Charge crossing the section per second is n e v_d A. (Key point: Formula)

2. What area must be used in the formula?
   A. 1 m^2
   B. 1 cm^2 = 10^-2 m^2
   C. 1 cm^2 = 10^-4 m^2
   D. 1 cm^2 = 10^-6 m^2
   Answer: C. 1 cm = 10^-2 m so 1 cm^2 = 10^-4 m^2. (Key point: Unit conversion)

3. The current is:
   A. 24 A
   B. 0.24 A
   C. 2.4 mA
   D. 2400 A
   Answer: B. I = 10^24 x 1.6e-19 x 1.5e-2 x 1e-4 = 0.24 A. (Key point: Result)

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