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​ = 0.25 ΩIa​ = 6 AM+−E = ?ωT

A DC motor runs from a 48 V supply and draws an armature current of 6 A. Its armature resistance is 0.25 Ω. Find the back-EMF E.

V = 48 VIa = 6 ARa = 0.25 Ω
E = V
2.Easy
+−110 VRa​M+−E = 102 Vn = 1000 rpmT

A DC motor turns at 1000 rpm, and its back-EMF at that speed is 102 V. Find the motor constant k in V·s/rad.

E = 102 Vn = 1000 rpm
k = V·s/rad
3.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 43 W. Find its efficiency η.

V = 110 VIa = 15 ARa = 1 ΩProt = 43 W
η = %
4.Medium
T (N·m)n (rpm)Tst​ = ?n0​

A DC motor with k = 1.5 N·m/A and Ra = 0.2 Ω is connected to 110 V. Find its stall torque Tstall, the torque at zero speed.

V = 110 Vk = 1.5 N·m/ARa = 0.2 Ω
Tstall = N·m
5.Hard
+−24 VRa​ = 4 ΩM+−EωT

A small DC motor has an armature resistance of 4 Ω and runs from 24 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 24 VRa = 4 Ω
Pmax = W
6.Hard
T (N·m)n (rpm)1.5 N·m500 rpm

A DC motor with k = 0.75 V·s/rad and Ra = 1.5 Ω must drive a load of 1.5 N·m at 500 rpm. Find the armature voltage V it needs.

k = 0.75 V·s/radRa = 1.5 ΩT = 1.5 N·mn = 500 rpm
V = V

Answer key

  1. 1. E = 46.5 V
  2. 2. k = 0.974 V·s/rad
  3. 3. η = 83.76 %
  4. 4. Tstall = 825 N·m
  5. 5. Pmax = 36 W
  6. 6. V = 42.27 V

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