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
+−110 VRa​ = 1 ΩIa​ = 4 AM+−E = ?ωT

A DC motor runs from a 110 V supply and draws an armature current of 4 A. Its armature resistance is 1 Ω. Find the back-EMF E.

V = 110 VIa = 4 ARa = 1 Ω
E = V
2.Easy
+−220 VRa​ = 0.5 ΩIa​ = 20 AM+−En = ?T

A DC motor with k = 2 V·s/rad and an armature resistance of 0.5 Ω runs from 220 V and draws 20 A. Find its speed n in rpm.

V = 220 VRa = 0.5 ΩIa = 20 Ak = 2 V·s/rad
n = rpm
3.Medium
+−48 VRa​ = 1.2 ΩIa​ = 4 AM+−EωT

A DC motor draws 4 A from a 48 V supply. Its armature resistance is 1.2 Ω and its rotational (friction, windage and iron) losses are 9 W. Find its efficiency η.

V = 48 VIa = 4 ARa = 1.2 ΩProt = 9 W
η = %
4.Medium
T (N·m)n (rpm)n0​ = ?

A DC motor with k = 0.75 V·s/rad runs from 120 V. Neglecting all losses at no load, find its no-load speed n0 in rpm.

V = 120 Vk = 0.75 V·s/rad
n0 = rpm
5.Hard
+−110 VRst​ = ?Ra​ = 1.2 Ω50 AM+−E = 0n = 0T

A 110 V DC motor has an armature resistance of 1.2 Ω. Find the series starting resistance Rst that limits the starting current to 50 A.

V = 110 VRa = 1.2 ΩImax = 50 A
Rst = Ω
6.Hard
+−110 VRa​ = 1 ΩM+−EωT

A small DC motor has an armature resistance of 1 Ω and runs from 110 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 110 VRa = 1 Ω
Pmax = W

Answer key

  1. 1. E = 106 V
  2. 2. n = 1003 rpm
  3. 3. η = 85.31 %
  4. 4. n0 = 1528 rpm
  5. 5. Rst = 1 Ω
  6. 6. Pmax = 3025 W

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