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​ = 0.4 ΩIa​ = 4 AM+−E = ?ωT

A DC motor runs from a 24 V supply and draws an armature current of 4 A. Its armature resistance is 0.4 Ω. Find the back-EMF E.

V = 24 VIa = 4 ARa = 0.4 Ω
E = V
2.Easy
+−48 VRa​ = 1.2 ΩIa​ = ?M+−E = 42 VωT

A DC motor on a 48 V supply has an armature resistance of 1.2 Ω. At its present speed the back-EMF is 42 V. Find the armature current Ia.

V = 48 VE = 42 VRa = 1.2 Ω
Ia = A
3.Medium
+−220 VRa​ = 0.25 ΩIa​ = 40 AM+−EωT

A DC motor draws 40 A from a 220 V supply. Its armature resistance is 0.25 Ω and its rotational (friction, windage and iron) losses are 336 W. Find its efficiency η.

V = 220 VIa = 40 ARa = 0.25 ΩProt = 336 W
η = %
4.Medium
T (N·m)n (rpm)60 N·mn0​n = ?

A DC motor (k = 2 N·m/A, Ra = 0.5 Ω) runs from 220 V and drives a load torque of 60 N·m. Find its speed n in rpm.

V = 220 Vk = 2 N·m/ARa = 0.5 ΩT = 60 N·m
n = rpm
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
+−120 VRa​ = 1 ΩM+−EωT

A small DC motor has an armature resistance of 1 Ω and runs from 120 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 120 VRa = 1 Ω
Pmax = W

Answer key

  1. 1. E = 22.4 V
  2. 2. Ia = 5 A
  3. 3. η = 91.64 %
  4. 4. n = 978.8 rpm
  5. 5. Pmax = 36 W
  6. 6. Pmax = 3600 W

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