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
+−24 VRa​ = 0.2 ΩIa​ = 4 AM+−En = ?T

A DC motor with k = 0.2 V·s/rad and an armature resistance of 0.2 Ω runs from 24 V and draws 4 A. Find its speed n in rpm.

V = 24 VRa = 0.2 ΩIa = 4 Ak = 0.2 V·s/rad
n = rpm
2.Easy
+−120 VRa​Ia​ = 25 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 25 A.

k = 1 N·m/AIa = 25 A
T = N·m
3.Medium
+−VRa​M+−En = 1000 rpmT = ?

A DC motor delivers 1 kW of mechanical power at 1000 rpm. Find the shaft torque T.

P = 1 kWn = 1000 rpm
T = N·m
4.Medium
+−48 VRa​ = 0.2 ΩIa​ = 20 AM+−EωT

A DC motor draws 20 A from a 48 V supply. Its armature resistance is 0.2 Ω and its rotational (friction, windage and iron) losses are 70 W. Find its efficiency η.

V = 48 VIa = 20 ARa = 0.2 ΩProt = 70 W
η = %
5.Hard
+−120 VRa​ = 0.8 ΩIa​: 15 → 7.5 AM+−En = ?T

A separately excited DC motor on 120 V (Ra = 0.8 Ω) runs at 900 rpm with an armature current of 15 A. The load changes and the current becomes 7.5 A, with the field unchanged. Find the new speed n2.

V = 120 VRa = 0.8 Ωn1 = 900 rpmIa1 = 15 AIa2 = 7.5 A
n2 = rpm
6.Hard
+−110 VRa​ = 4 ΩM+−EωT

A small DC motor has an armature resistance of 4 Ω and runs from 110 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 110 VRa = 4 Ω
Pmax = W

Answer key

  1. 1. n = 1108 rpm
  2. 2. T = 25 N·m
  3. 3. T = 9.549 N·m
  4. 4. η = 84.38 %
  5. 5. n2 = 950 rpm
  6. 6. Pmax = 756.3 W

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