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
+−110 VRa​ = 1.2 ΩIa​ = 10 AM+−E = ?ωT

A DC motor runs from a 110 V supply and draws an armature current of 10 A. Its armature resistance is 1.2 Ω. Find the back-EMF E.

V = 110 VIa = 10 ARa = 1.2 Ω
E = V
2.Easy
+−48 VRa​Ia​ = 12 AM+−EωT = ?

A permanent-magnet DC motor has the torque constant k = 0.3 N·m/A. Find the torque T it develops at an armature current of 12 A.

k = 0.3 N·m/AIa = 12 A
T = N·m
3.Medium
T (N·m)n (rpm)n0​ = ?

A DC motor with k = 0.3 V·s/rad runs from 120 V. Neglecting all losses at no load, find its no-load speed n0 in rpm.

V = 120 Vk = 0.3 V·s/rad
n0 = rpm
4.Medium
+−120 VRa​ = 0.5 ΩIa​ = 30 AM+−EωT

A DC motor draws 30 A from a 120 V supply. Its armature resistance is 0.5 Ω and its rotational (friction, windage and iron) losses are 189 W. Find its efficiency η.

V = 120 VIa = 30 ARa = 0.5 ΩProt = 189 W
η = %
5.Hard
T (N·m)n (rpm)0.6 N·m1200 rpm

A DC motor with k = 0.12 V·s/rad and Ra = 0.25 Ω must drive a load of 0.6 N·m at 1200 rpm. Find the armature voltage V it needs.

k = 0.12 V·s/radRa = 0.25 ΩT = 0.6 N·mn = 1200 rpm
V = V
6.Hard
+−24 VRa​ = 1.2 ΩM+−EωT

A small DC motor has an armature resistance of 1.2 Ω and runs from 24 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 24 VRa = 1.2 Ω
Pmax = W

Answer key

  1. 1. E = 98 V
  2. 2. T = 3.6 N·m
  3. 3. n0 = 3820 rpm
  4. 4. η = 82.25 %
  5. 5. V = 16.33 V
  6. 6. Pmax = 120 W

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