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​ = 0.5 ΩIa​ = 15 AM+−E = ?ωT

A DC motor runs from a 220 V supply and draws an armature current of 15 A. Its armature resistance is 0.5 Ω. Find the back-EMF E.

V = 220 VIa = 15 ARa = 0.5 Ω
E = V
2.Easy
+−120 VRa​ = 2 ΩIa​ = 2 AM+−En = ?T

A DC motor with k = 0.8 V·s/rad and an armature resistance of 2 Ω runs from 120 V and draws 2 A. Find its speed n in rpm.

V = 120 VRa = 2 ΩIa = 2 Ak = 0.8 V·s/rad
n = rpm
3.Medium
+−120 VRa​ = 1.2 ΩIa​ = 8 AM+−EωT

A DC motor draws 8 A from a 120 V supply. Its armature resistance is 1.2 Ω and its rotational (friction, windage and iron) losses are 44 W. Find its efficiency η.

V = 120 VIa = 8 ARa = 1.2 ΩProt = 44 W
η = %
4.Medium
+−VRa​M+−En = 1200 rpmT = ?

A DC motor delivers 0.5 kW of mechanical power at 1200 rpm. Find the shaft torque T.

P = 0.5 kWn = 1200 rpm
T = N·m
5.Hard
T (N·m)n (rpm)24 N·m750 rpm

A DC motor with k = 0.8 V·s/rad and Ra = 0.4 Ω must drive a load of 24 N·m at 750 rpm. Find the armature voltage V it needs.

k = 0.8 V·s/radRa = 0.4 ΩT = 24 N·mn = 750 rpm
V = V
6.Hard
+−110 VRa​ = 0.5 ΩM+−En = ?T = 22.5 N·m

A separately excited DC motor (k = 1.5 V·s/rad at full field, Ra = 0.5 Ω, V = 110 V) drives a constant load torque of 22.5 N·m. The field flux is reduced to 85 % of its full value. Find the new speed n.

V = 110 Vk = 1.5 V·s/radRa = 0.5 ΩT = 22.5 N·mΦ = 85 %
n = rpm

Answer key

  1. 1. E = 212.5 V
  2. 2. n = 1385 rpm
  3. 3. η = 87.42 %
  4. 4. T = 3.979 N·m
  5. 5. V = 74.83 V
  6. 6. n = 757.8 rpm

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