---
title: "Series motor speed with 6 ohm series resistance"
subject: "Electrical Machines"
chapter: 4
key: "semester_4/electrical_machines:dcm-series-resistance-speed-1000rpm-6ohm"
source: https://www.bctengineer.com/q/semester_4/electrical_machines/dcm-series-resistance-speed-1000rpm-6ohm
site: BCT Engineering
---

# Series motor speed with 6 ohm series resistance

Electrical Machines · Chapter 4: DC Motor

- Asked in: 2070 Bhadra, 5 marks
- Video: [speed control of Dc series mathod](https://www.youtube.com/watch?v=av_V0iXFdzo) — Micro Teach
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines/dcm-series-resistance-speed-1000rpm-6ohm
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-4

## Question

A DC series motor of resistance $1\ \Omega$ 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 $6\ \Omega$ resistance and taking the same current at the same supply voltage.

## Short answer

With same current, flux remains constant. At 1000 rpm, Eb = 230 V; with added 6 Ω total resistance 7 Ω, Eb = 110 V. Speed = 478.3 rpm.

## Answer

The current is the same in both cases, so the flux is the same ($\Phi\propto I$). Hence $N\propto E_b$.

**Case 1:** 1000 rpm, 250 V, 20 A, $R = 1\ \Omega$ (armature plus series field).

$$
E_{b1} = V - IR = 250 - 20(1) = 230\ \text{V}
$$

**Case 2:** extra series resistance 6 Ω, so total $R = 1 + 6 = 7\ \Omega$ and the same $I = 20$ A.

$$
E_{b2} = 250 - 20(7) = 110\ \text{V}
$$

$$
N_2 = N_1\frac{E_{b2}}{E_{b1}} = 1000\times\frac{110}{230} = 478.3\ \text{rpm}
$$

**Answer:** the motor runs at $478.3\ \text{rpm}$.

## Check yourself

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

1. Why is N proportional to Eb here?
   A. Current is the same, so flux (proportional to I) is the same
   B. Voltage is different
   C. Resistance is the same
   D. Speed is the same
   Answer: A. Series flux depends on current, which is unchanged. (Key point: Same current same flux)

2. Eb1 with R = 1 ohm, 20 A, 250 V is:
   A. 250 V
   B. 220 V
   C. 240 V
   D. 230 V
   Answer: D. 250 - 20 x 1 = 230 V. (Key point: Case 1 back emf)

3. With 6 ohm added, the total resistance and Eb2 are:
   A. 6 ohm, 130 V
   B. 7 ohm, 110 V
   C. 7 ohm, 130 V
   D. 1 ohm, 230 V
   Answer: B. Total = 1 + 6 = 7 ohm; Eb2 = 250 - 20 x 7 = 110 V. (Key point: Case 2 resistance)

4. The new speed is:
   A. 1000 rpm
   B. 1000 x 230/110
   C. 478.3 rpm
   D. 520 rpm
   Answer: C. 1000 x 110/230 = 478.3 rpm. (Key point: New speed)

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## Related in other subjects

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