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​M+−E = 100 Vn = 1000 rpmT

A DC motor turns at 1000 rpm, and its back-EMF at that speed is 100 V. Find the motor constant k in V·s/rad.

E = 100 Vn = 1000 rpm
k = V·s/rad
2.Easy
+−240 VRa​ = 1 ΩIa​ = ?M+−E = 230 VωT

A DC motor on a 240 V supply has an armature resistance of 1 Ω. At its present speed the back-EMF is 230 V. Find the armature current Ia.

V = 240 VE = 230 VRa = 1 Ω
Ia = A
3.Medium
+−120 VRa​ = 0.5 ΩIa​ = 8 AM+−EωT

A DC motor draws 8 A from a 120 V supply. Its armature resistance is 0.5 Ω and its rotational (friction, windage and iron) losses are 28 W. Find its efficiency η.

V = 120 VIa = 8 ARa = 0.5 ΩProt = 28 W
η = %
4.Medium
+−24 VRa​ = 0.2 ΩIa​ = 8 AM+−EωT

A DC motor draws 8 A from a 24 V supply. Its armature resistance is 0.2 Ω and its rotational (friction, windage and iron) losses are 9 W. Find its efficiency η.

V = 24 VIa = 8 ARa = 0.2 ΩProt = 9 W
η = %
5.Hard
+−120 VRs​ = ?Ra​ = 0.5 ΩM+−En = 300 rpmT = 15 N·m

A DC motor (k = 1.5 V·s/rad, Ra = 0.5 Ω) on a fixed 120 V supply drives a load of 15 N·m. Find the series resistance Rs that slows it down to 300 rpm.

V = 120 Vk = 1.5 V·s/radRa = 0.5 ΩT = 15 N·mn = 300 rpm
Rs = Ω
6.Hard
+−110 VRa​ = 2 ΩM+−EωT

A small DC motor has an armature resistance of 2 Ω and runs from 110 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 110 VRa = 2 Ω
Pmax = W

Answer key

  1. 1. k = 0.9549 V·s/rad
  2. 2. Ia = 10 A
  3. 3. η = 93.75 %
  4. 4. η = 88.65 %
  5. 5. Rs = 6.788 Ω
  6. 6. Pmax = 1513 W

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