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
+−220 VRa​ = 1.5 ΩIa​ = 8 AM+−E = ?ωT

A DC motor runs from a 220 V supply and draws an armature current of 8 A. Its armature resistance is 1.5 Ω. Find the back-EMF E.

V = 220 VIa = 8 ARa = 1.5 Ω
E = V
2.Easy
+−24 VRa​ = 0.2 ΩIa​ = ?M+−E = 0n = 0T

A DC motor with an armature resistance of 0.2 Ω is switched directly onto a 24 V supply. Its normal full-load current is 12 A. Find the armature current Istart at the moment of starting.

V = 24 VRa = 0.2 Ω
Istart = A
3.Medium
+−240 VRa​ = 0.4 ΩIa​ = 20 AM+−EωT

A DC motor draws 20 A from a 240 V supply. Its armature resistance is 0.4 Ω and its rotational (friction, windage and iron) losses are 139 W. Find its efficiency η.

V = 240 VIa = 20 ARa = 0.4 ΩProt = 139 W
η = %
4.Medium
T (N·m)n (rpm)n0​ = ?

A DC motor with k = 1.5 V·s/rad runs from 240 V. Neglecting all losses at no load, find its no-load speed n0 in rpm.

V = 240 Vk = 1.5 V·s/rad
n0 = rpm
5.Hard
+−48 VRa​ = 1.2 ΩM+−EωT

A small DC motor has an armature resistance of 1.2 Ω and runs from 48 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 48 VRa = 1.2 Ω
Pmax = W
6.Hard
T (N·m)n (rpm)12 N·m600 rpm

A DC motor with k = 1 V·s/rad and Ra = 1.5 Ω must drive a load of 12 N·m at 600 rpm. Find the armature voltage V it needs.

k = 1 V·s/radRa = 1.5 ΩT = 12 N·mn = 600 rpm
V = V

Answer key

  1. 1. E = 208 V
  2. 2. Istart = 120 A
  3. 3. η = 93.77 %
  4. 4. n0 = 1528 rpm
  5. 5. Pmax = 480 W
  6. 6. V = 80.83 V

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