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
+−240 VRa​M+−E = 216 Vn = 900 rpmT

A DC motor turns at 900 rpm, and its back-EMF at that speed is 216 V. Find the motor constant k in V·s/rad.

E = 216 Vn = 900 rpm
k = V·s/rad
2.Easy
+−48 VRa​ = 0.8 ΩIa​ = 4 AM+−EωT

A DC motor runs from 48 V with an armature current of 4 A. The armature resistance is 0.8 Ω. Find the developed (electromagnetic) power Pdev.

V = 48 VIa = 4 ARa = 0.8 Ω
Pdev = W
3.Medium
T (N·m)n (rpm)30 N·mn0​nFL​

A DC motor (k = 1.2 V·s/rad, Ra = 0.2 Ω) runs from 120 V. At full load it draws 25 A. Neglecting the no-load current, find its speed regulation SR = (n₀ − nFL)/nFL in percent.

V = 120 Vk = 1.2 V·s/radRa = 0.2 ΩIFL = 25 A
SR = %
4.Medium
+−120 VRa​ = 0.4 ΩIa​ = 20 AM+−EωT

A DC motor draws 20 A from a 120 V supply. Its armature resistance is 0.4 Ω and its rotational (friction, windage and iron) losses are 134 W. Find its efficiency η.

V = 120 VIa = 20 ARa = 0.4 ΩProt = 134 W
η = %
5.Hard
T (N·m)n (rpm)3 N·m750 rpm

A DC motor with k = 0.5 V·s/rad and Ra = 2 Ω must drive a load of 3 N·m at 750 rpm. Find the armature voltage V it needs.

k = 0.5 V·s/radRa = 2 ΩT = 3 N·mn = 750 rpm
V = V
6.Hard
+−24 VRa​ = 1 ΩM+−EωT

A small DC motor has an armature resistance of 1 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 Ω
Pmax = W

Answer key

  1. 1. k = 2.292 V·s/rad
  2. 2. Pdev = 179.2 W
  3. 3. SR = 4.348 %
  4. 4. η = 87.75 %
  5. 5. V = 51.27 V
  6. 6. Pmax = 144 W

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