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 = 208 Vn = 2400 rpmT

A DC motor turns at 2400 rpm, and its back-EMF at that speed is 208 V. Find the motor constant k in V·s/rad.

E = 208 Vn = 2400 rpm
k = V·s/rad
2.Easy
+−120 VRa​ = 2 ΩIa​ = 2 AM+−En = ?T

A DC motor with k = 0.6 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 = 0.6 V·s/rad
n = rpm
3.Medium
+−110 VRa​ = 0.8 ΩIa​ = 8 AM+−EωT

A DC motor draws 8 A from a 110 V supply. Its armature resistance is 0.8 Ω and its rotational (friction, windage and iron) losses are 66 W. Find its efficiency η.

V = 110 VIa = 8 ARa = 0.8 ΩProt = 66 W
η = %
4.Medium
+−VRa​M+−En = 2000 rpmT = ?

A DC motor delivers 15 kW of mechanical power at 2000 rpm. Find the shaft torque T.

P = 15 kWn = 2000 rpm
T = N·m
5.Hard
+−48 VRa​ = 0.5 ΩM+−EωT

A small DC motor has an armature resistance of 0.5 Ω and runs from 48 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 48 VRa = 0.5 Ω
Pmax = W
6.Hard
T (N·m)n (rpm)6 N·m400 rpm

A DC motor with k = 0.75 V·s/rad and Ra = 1 Ω must drive a load of 6 N·m at 400 rpm. Find the armature voltage V it needs.

k = 0.75 V·s/radRa = 1 ΩT = 6 N·mn = 400 rpm
V = V

Answer key

  1. 1. k = 0.8276 V·s/rad
  2. 2. n = 1846 rpm
  3. 3. η = 86.68 %
  4. 4. T = 71.62 N·m
  5. 5. Pmax = 1152 W
  6. 6. V = 39.42 V

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