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​ = 0.25 ΩIa​ = ?M+−E = 115 VωT

A DC motor on a 120 V supply has an armature resistance of 0.25 Ω. At its present speed the back-EMF is 115 V. Find the armature current Ia.

V = 120 VE = 115 VRa = 0.25 Ω
Ia = A
2.Easy
+−240 VRa​ = 1.5 ΩIa​ = ?M+−E = 222 VωT

A DC motor on a 240 V supply has an armature resistance of 1.5 Ω. At its present speed the back-EMF is 222 V. Find the armature current Ia.

V = 240 VE = 222 VRa = 1.5 Ω
Ia = A
3.Medium
+−48 VRa​ = 0.4 ΩIa​ = 5 AM+−EωT

A DC motor draws 5 A from a 48 V supply. Its armature resistance is 0.4 Ω and its rotational (friction, windage and iron) losses are 9 W. Find its efficiency η.

V = 48 VIa = 5 ARa = 0.4 ΩProt = 9 W
η = %
4.Medium
T (N·m)n (rpm)6 N·mn0​n = ?

A DC motor (k = 0.5 N·m/A, Ra = 0.4 Ω) runs from 48 V and drives a load torque of 6 N·m. Find its speed n in rpm.

V = 48 Vk = 0.5 N·m/ARa = 0.4 ΩT = 6 N·m
n = rpm
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​ = 1.2 ΩM+−EωT

A small DC motor has an armature resistance of 1.2 Ω and runs from 24 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 24 VRa = 1.2 Ω
Pmax = W

Answer key

  1. 1. Ia = 20 A
  2. 2. Ia = 12 A
  3. 3. η = 92.08 %
  4. 4. n = 825.1 rpm
  5. 5. Pmax = 384 W
  6. 6. Pmax = 120 W

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