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
+−120 VRa​Ia​ = 12 AM+−EωT = ?

A permanent-magnet DC motor has the torque constant k = 0.4 N·m/A. Find the torque T it develops at an armature current of 12 A.

k = 0.4 N·m/AIa = 12 A
T = N·m
2.Easy
+−24 VRa​ = 0.2 ΩIa​ = 6 AM+−En = ?T

A DC motor with k = 0.15 V·s/rad and an armature resistance of 0.2 Ω runs from 24 V and draws 6 A. Find its speed n in rpm.

V = 24 VRa = 0.2 ΩIa = 6 Ak = 0.15 V·s/rad
n = rpm
3.Medium
T (N·m)n (rpm)n0​ = ?

A DC motor with k = 0.15 V·s/rad runs from 24 V. Neglecting all losses at no load, find its no-load speed n0 in rpm.

V = 24 Vk = 0.15 V·s/rad
n0 = rpm
4.Medium
+−240 VRa​ = 0.4 ΩIa​ = 25 AM+−EωT

A DC motor draws 25 A from a 240 V supply. Its armature resistance is 0.4 Ω and its rotational (friction, windage and iron) losses are 345 W. Find its efficiency η.

V = 240 VIa = 25 ARa = 0.4 ΩProt = 345 W
η = %
5.Hard
+−240 VRa​ = 0.8 ΩIa​: 10 → 20 AM+−En = ?T

A separately excited DC motor on 240 V (Ra = 0.8 Ω) runs at 1200 rpm with an armature current of 10 A. The load changes and the current becomes 20 A, with the field unchanged. Find the new speed n2.

V = 240 VRa = 0.8 Ωn1 = 1200 rpmIa1 = 10 AIa2 = 20 A
n2 = rpm
6.Hard
+−120 VRa​ = 1 ΩM+−EωT

A small DC motor has an armature resistance of 1 Ω and runs from 120 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 120 VRa = 1 Ω
Pmax = W

Answer key

  1. 1. T = 4.8 N·m
  2. 2. n = 1451 rpm
  3. 3. n0 = 1528 rpm
  4. 4. η = 90.08 %
  5. 5. n2 = 1159 rpm
  6. 6. Pmax = 3600 W

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