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​ = 8 AM+−EωT = ?

A permanent-magnet DC motor has the torque constant k = 1 N·m/A. Find the torque T it develops at an armature current of 8 A.

k = 1 N·m/AIa = 8 A
T = N·m
2.Easy
+−110 VRa​Ia​ = 5 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 5 A.

k = 0.4 N·m/AIa = 5 A
T = N·m
3.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
4.Medium
+−110 VRa​ = 1 ΩIa​ = 15 AM+−EωT

A DC motor draws 15 A from a 110 V supply. Its armature resistance is 1 Ω and its rotational (friction, windage and iron) losses are 71 W. Find its efficiency η.

V = 110 VIa = 15 ARa = 1 ΩProt = 71 W
η = %
5.Hard
+−220 VRst​ = ?Ra​ = 1.5 Ω20 AM+−E = 0n = 0T

A 220 V DC motor has an armature resistance of 1.5 Ω. Find the series starting resistance Rst that limits the starting current to 20 A.

V = 220 VRa = 1.5 ΩImax = 20 A
Rst = Ω
6.Hard
+−24 VRa​ = 0.8 ΩIa​: 2 → 1.2 AM+−En = ?T

A separately excited DC motor on 24 V (Ra = 0.8 Ω) runs at 900 rpm with an armature current of 2 A. The load changes and the current becomes 1.2 A, with the field unchanged. Find the new speed n2.

V = 24 VRa = 0.8 Ωn1 = 900 rpmIa1 = 2 AIa2 = 1.2 A
n2 = rpm

Answer key

  1. 1. T = 8 N·m
  2. 2. T = 2 N·m
  3. 3. n0 = 1528 rpm
  4. 4. η = 82.06 %
  5. 5. Rst = 9.5 Ω
  6. 6. n2 = 925.7 rpm

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