---
title: "Series motor speed with 6 Ω in series"
subject: "Electrical Machine"
chapter: 4
key: "semester_4/electrical_machine:series-motor-1ohm-6ohm-series"
source: https://www.bctengineer.com/q/semester_4/electrical_machine/series-motor-1ohm-6ohm-series
site: BCT Engineering
---

# Series motor speed with 6 Ω in series

Electrical Machine · Chapter 4: DC Motor

- Asked in: 2070 Bhadra, 5 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machine/series-motor-1ohm-6ohm-series
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-4

## Question

A dc series motor of resistance 1 Ω between terminals runs at 1,000 RPM at 250 V with a current of 20 A. Find the speed at which it will run when connected in series with a 6 Ω resistance and taking the same current at the same supply voltage.

## Short answer

With same current and supply voltage, flux is constant, so speed is proportional to back emf. Eb drops from 230 V to 110 V due to added 6 Ω resistance, giving speed ≈ 478 rpm.

## Answer

For a series motor with the same current and the same supply, the flux is unchanged (Φ ∝ I), so the speed is proportional to the back emf.

#### Equivalent circuit
```text
 Case 1: V --[1 ohm (Ra+Rse)]--(Eb1)       I = 20 A
 Case 2: V --[1 ohm]--[6 ohm ext]--(Eb2)   I = 20 A
```

#### Case 1
E_b1 = V − I R = 250 − 20 × 1 = 230 V at N₁ = 1000 rpm

#### Case 2 (extra 6 Ω, same current 20 A)
E_b2 = 250 − 20 × (1 + 6) = 250 − 140 = 110 V

#### Speed
N₂ / N₁ = E_b2 / E_b1 (same Φ)

N₂ = 1000 × 110 / 230 = **478.3 rpm**

**Answer: the motor will run at about 478 rpm.**

## Check yourself

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

1. Why is the flux unchanged in the second case?
   A. The current is the same and Φ ∝ I
   B. The speed is the same
   C. The resistance is the same
   D. The voltage is the same
   Answer: A. Series flux depends on current, which is 20 A in both cases. (Key point: Flux with same current)

2. What is E_b1?
   A. 250 V
   B. 230 V
   C. 110 V
   D. 270 V
   Answer: B. 250 - 20 × 1 = 230 V. (Key point: Case 1 back emf)

3. What is E_b2 with the extra 6 Ω?
   A. 250 V
   B. 230 V
   C. 110 V
   D. 130 V
   Answer: C. 250 - 20 × 7 = 110 V. (Key point: Case 2 back emf)

4. What is the new speed?
   A. 220 rpm
   B. 1000 rpm
   C. 1200 rpm
   D. 478 rpm
   Answer: D. N2 = 1000 × 110/230 = 478.3 rpm. (Key point: Speed)

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