DC motors worksheet with answers

Free printable DC motors worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
+−48 VRa​ = 0.4 ΩIa​ = 5 AM+−E = ?ωT

A DC motor runs from a 48 V supply and draws an armature current of 5 A. Its armature resistance is 0.4 Ω. Find the back-EMF E.

V = 48 VIa = 5 ARa = 0.4 Ω
E = V
2.Easy
+−48 VRa​ = 0.8 ΩIa​ = ?M+−E = 44 VωT

A DC motor on a 48 V supply has an armature resistance of 0.8 Ω. At its present speed the back-EMF is 44 V. Find the armature current Ia.

V = 48 VE = 44 VRa = 0.8 Ω
Ia = A
3.Medium
T (N·m)n (rpm)n0​ = ?

A DC motor with k = 0.12 V·s/rad runs from 24 V. Neglecting all losses at no load, find its no-load speed n0 in rpm.

V = 24 Vk = 0.12 V·s/rad
n0 = rpm
4.Medium
+−48 VRa​ = 0.4 ΩIa​ = 8 AM+−EωT

A DC motor draws 8 A from a 48 V supply. Its armature resistance is 0.4 Ω and its rotational (friction, windage and iron) losses are 29 W. Find its efficiency η.

V = 48 VIa = 8 ARa = 0.4 ΩProt = 29 W
η = %
5.Hard
+−24 VRs​ = ?Ra​ = 1 ΩM+−En = 1200 rpmT = 0.3 N·m

A DC motor (k = 0.15 V·s/rad, Ra = 1 Ω) on a fixed 24 V supply drives a load of 0.3 N·m. Find the series resistance Rs that slows it down to 1200 rpm.

V = 24 Vk = 0.15 V·s/radRa = 1 ΩT = 0.3 N·mn = 1200 rpm
Rs = Ω
6.Hard
T (N·m)n (rpm)6 N·m400 rpm

A DC motor with k = 1.2 V·s/rad and Ra = 1.2 Ω must drive a load of 6 N·m at 400 rpm. Find the armature voltage V it needs.

k = 1.2 V·s/radRa = 1.2 ΩT = 6 N·mn = 400 rpm
V = V

Answer key

  1. 1. E = 46 V
  2. 2. Ia = 5 A
  3. 3. n0 = 1910 rpm
  4. 4. η = 85.78 %
  5. 5. Rs = 1.575 Ω
  6. 6. V = 56.27 V

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