---
title: "Ratio of drift velocities, series and parallel"
subject: "Engineering Physics"
chapter: 8
key: "semester_1/engineering_physics:drift-velocity-ratio-series-parallel"
source: https://www.bctengineer.com/q/semester_1/engineering_physics/drift-velocity-ratio-series-parallel
site: BCT Engineering
---

# Ratio of drift velocities, series and parallel

Engineering Physics · Chapter 8: Electromagnetism

- Asked in: 2068 Shrawan, 5 marks
- Video: [Drift velicity in series – Parallel Combination of unidentical Conductors](https://www.youtube.com/watch?v=W3fdA24T-bQ) — M Asif Physics
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/engineering_physics/drift-velocity-ratio-series-parallel
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-8

## Question

Two copper wires of same length l and cross sectional areas A and 2A are connected to a battery. What will be the ratio of drift velocities when the wires are in (a) series and (b) parallel?

## Short answer

In series, same I, v_d = I/(nAe) → v₁/v₂ = A₂/A₁ = 2:1. In parallel, same length so same electric field, v_d = μE equal, so v₁:v₂ = 1:1.

## Answer

Wire 1 has area A and wire 2 has area 2A. Both have the same length l and are copper, so the same n and resistivity ρ. Drift velocity is v_d = I/(nAe) = J/(ne).

#### (a) In series
The same current I flows in both wires.

```text
v₁ = I/(n A e) ;  v₂ = I/(n 2A e)
v₁ / v₂ = 2A / A = 2
```

**Answer: v₁ : v₂ = 2 : 1** (the thinner wire has twice the drift speed).

#### (b) In parallel
The same potential difference V is across both wires, and they have the same length, so the same electric field E = V/l.

```text
v_d = μ E   (same material, same μ, same E)
v₁ = v₂
```

Check with currents: I₁ = V/R₁ with R₁ = ρl/A, so I₁ = VA/(ρl) and I₂ = 2VA/(ρl). Then v₁ = I₁/(nAe) = V/(ρ l n e) and v₂ = I₂/(n 2A e) = V/(ρ l n e). Equal.

**Answer: v₁ : v₂ = 1 : 1** (equal drift speeds).

## Check yourself

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

1. For wires in series, which quantity is the same?
   A. The current
   B. The potential difference
   C. The drift velocity
   D. The current density
   Answer: A. Series elements carry the same current. (Key point: Series current)

2. In series with areas A and 2A, v₁ : v₂ is:
   A. 1 : 2
   B. 2 : 1
   C. 1 : 1
   D. 4 : 1
   Answer: B. v = I/(nAe), so v ∝ 1/A. (Key point: Series ratio)

3. Wires of equal length in parallel have the same:
   A. current
   B. current density
   C. electric field E = V/l
   D. resistance
   Answer: C. Same V and same length give the same E. (Key point: Parallel field)

4. In parallel, v₁ : v₂ is:
   A. 2 : 1
   B. 1 : 2
   C. 1 : 4
   D. 1 : 1, since v_d = μE
   Answer: D. Same material and same E give same drift speed. (Key point: Parallel ratio)

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