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​M+−E = 110 Vn = 1200 rpmT

A DC motor turns at 1200 rpm, and its back-EMF at that speed is 110 V. Find the motor constant k in V·s/rad.

E = 110 Vn = 1200 rpm
k = V·s/rad
2.Easy
+−110 VRa​Ia​ = 5 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 5 A.

k = 1 N·m/AIa = 5 A
T = N·m
3.Medium
T (N·m)n (rpm)Tst​ = ?n0​

A DC motor with k = 0.15 N·m/A and Ra = 0.5 Ω is connected to 48 V. Find its stall torque Tstall, the torque at zero speed.

V = 48 Vk = 0.15 N·m/ARa = 0.5 Ω
Tstall = N·m
4.Medium
+−110 VRa​ = 1 ΩIa​ = 8 AM+−EωT

A DC motor draws 8 A from a 110 V supply. Its armature resistance is 1 Ω and its rotational (friction, windage and iron) losses are 33 W. Find its efficiency η.

V = 110 VIa = 8 ARa = 1 ΩProt = 33 W
η = %
5.Hard
+−48 VRa​ = 1.5 ΩM+−EωT

A small DC motor has an armature resistance of 1.5 Ω and runs from 48 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 48 VRa = 1.5 Ω
Pmax = W
6.Hard
+−24 VRa​ = 3 ΩM+−EωT

A small DC motor has an armature resistance of 3 Ω and runs from 24 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 24 VRa = 3 Ω
Pmax = W

Answer key

  1. 1. k = 0.8754 V·s/rad
  2. 2. T = 5 N·m
  3. 3. Tstall = 14.4 N·m
  4. 4. η = 88.98 %
  5. 5. Pmax = 384 W
  6. 6. Pmax = 48 W

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