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
+−240 VRa​ = 2 ΩIa​ = 10 AM+−E = ?ωT

A DC motor runs from a 240 V supply and draws an armature current of 10 A. Its armature resistance is 2 Ω. Find the back-EMF E.

V = 240 VIa = 10 ARa = 2 Ω
E = V
2.Easy
+−48 VRa​M+−E = 43 Vn = 1200 rpmT

A DC motor turns at 1200 rpm, and its back-EMF at that speed is 43 V. Find the motor constant k in V·s/rad.

E = 43 Vn = 1200 rpm
k = V·s/rad
3.Medium
+−220 VRa​ = 0.8 ΩIa​ = 12 AM+−EωT

A DC motor draws 12 A from a 220 V supply. Its armature resistance is 0.8 Ω and its rotational (friction, windage and iron) losses are 151 W. Find its efficiency η.

V = 220 VIa = 12 ARa = 0.8 ΩProt = 151 W
η = %
4.Medium
+−VRa​M+−En = 1500 rpmT = ?

A DC motor delivers 2.2 kW of mechanical power at 1500 rpm. Find the shaft torque T.

P = 2.2 kWn = 1500 rpm
T = N·m
5.Hard
T (N·m)n (rpm)10 N·m400 rpm

A DC motor with k = 1 V·s/rad and Ra = 1 Ω must drive a load of 10 N·m at 400 rpm. Find the armature voltage V it needs.

k = 1 V·s/radRa = 1 ΩT = 10 N·mn = 400 rpm
V = V
6.Hard
T (N·m)n (rpm)0.4 N·m800 rpm

A DC motor with k = 0.2 V·s/rad and Ra = 2 Ω must drive a load of 0.4 N·m at 800 rpm. Find the armature voltage V it needs.

k = 0.2 V·s/radRa = 2 ΩT = 0.4 N·mn = 800 rpm
V = V

Answer key

  1. 1. E = 220 V
  2. 2. k = 0.3422 V·s/rad
  3. 3. η = 89.92 %
  4. 4. T = 14.01 N·m
  5. 5. V = 51.89 V
  6. 6. V = 20.76 V

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