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
+−220 VRa​M+−E = 211 Vn = 600 rpmT

A DC motor turns at 600 rpm, and its back-EMF at that speed is 211 V. Find the motor constant k in V·s/rad.

E = 211 Vn = 600 rpm
k = V·s/rad
2.Easy
+−240 VRa​ = 0.8 ΩIa​ = ?M+−E = 220 VωT

A DC motor on a 240 V supply has an armature resistance of 0.8 Ω. At its present speed the back-EMF is 220 V. Find the armature current Ia.

V = 240 VE = 220 VRa = 0.8 Ω
Ia = A
3.Medium
+−220 VRa​ = 0.4 ΩIa​ = 20 AM+−EωT

A DC motor draws 20 A from a 220 V supply. Its armature resistance is 0.4 Ω and its rotational (friction, windage and iron) losses are 170 W. Find its efficiency η.

V = 220 VIa = 20 ARa = 0.4 ΩProt = 170 W
η = %
4.Medium
+−110 VRa​ = 1 ΩIa​ = 12 AM+−EωT

A DC motor draws 12 A from a 110 V supply. Its armature resistance is 1 Ω and its rotational (friction, windage and iron) losses are 35 W. Find its efficiency η.

V = 110 VIa = 12 ARa = 1 ΩProt = 35 W
η = %
5.Hard
+−220 VRs​ = ?Ra​ = 0.25 ΩM+−En = 300 rpmT = 36 N·m

A DC motor (k = 1.2 V·s/rad, Ra = 0.25 Ω) on a fixed 220 V supply drives a load of 36 N·m. Find the series resistance Rs that slows it down to 300 rpm.

V = 220 Vk = 1.2 V·s/radRa = 0.25 ΩT = 36 N·mn = 300 rpm
Rs = Ω
6.Hard
+−120 VRs​ = ?Ra​ = 0.25 ΩM+−En = 800 rpmT = 9 N·m

A DC motor (k = 0.3 V·s/rad, Ra = 0.25 Ω) on a fixed 120 V supply drives a load of 9 N·m. Find the series resistance Rs that slows it down to 800 rpm.

V = 120 Vk = 0.3 V·s/radRa = 0.25 ΩT = 9 N·mn = 800 rpm
Rs = Ω

Answer key

  1. 1. k = 3.358 V·s/rad
  2. 2. Ia = 25 A
  3. 3. η = 92.5 %
  4. 4. η = 86.44 %
  5. 5. Rs = 5.827 Ω
  6. 6. Rs = 2.912 Ω

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