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
+−48 VRa​Ia​ = 10 AM+−EωT = ?

A permanent-magnet DC motor has the torque constant k = 1.5 N·m/A. Find the torque T it develops at an armature current of 10 A.

k = 1.5 N·m/AIa = 10 A
T = N·m
2.Easy
+−240 VRa​M+−E = 210 Vn = 3000 rpmT

A DC motor turns at 3000 rpm, and its back-EMF at that speed is 210 V. Find the motor constant k in V·s/rad.

E = 210 Vn = 3000 rpm
k = V·s/rad
3.Medium
T (N·m)n (rpm)Tst​ = ?n0​

A DC motor with k = 0.4 N·m/A and Ra = 0.5 Ω is connected to 110 V. Find its stall torque Tstall, the torque at zero speed.

V = 110 Vk = 0.4 N·m/ARa = 0.5 Ω
Tstall = N·m
4.Medium
+−240 VRa​ = 0.25 ΩIa​ = 50 AM+−EωT

A DC motor draws 50 A from a 240 V supply. Its armature resistance is 0.25 Ω and its rotational (friction, windage and iron) losses are 910 W. Find its efficiency η.

V = 240 VIa = 50 ARa = 0.25 ΩProt = 910 W
η = %
5.Hard
T (N·m)n (rpm)2.25 N·m1500 rpm

A DC motor with k = 0.15 V·s/rad and Ra = 0.25 Ω must drive a load of 2.25 N·m at 1500 rpm. Find the armature voltage V it needs.

k = 0.15 V·s/radRa = 0.25 ΩT = 2.25 N·mn = 1500 rpm
V = V
6.Hard
+−220 VRa​ = 2 ΩIa​: 6 → 1.5 AM+−En = ?T

A separately excited DC motor on 220 V (Ra = 2 Ω) runs at 1500 rpm with an armature current of 6 A. The load changes and the current becomes 1.5 A, with the field unchanged. Find the new speed n2.

V = 220 VRa = 2 Ωn1 = 1500 rpmIa1 = 6 AIa2 = 1.5 A
n2 = rpm

Answer key

  1. 1. T = 15 N·m
  2. 2. k = 0.6685 V·s/rad
  3. 3. Tstall = 88 N·m
  4. 4. η = 87.21 %
  5. 5. V = 27.31 V
  6. 6. n2 = 1565 rpm

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