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​Ia​ = 20 AM+−EωT = ?

A permanent-magnet DC motor has the torque constant k = 0.08 N·m/A. Find the torque T it develops at an armature current of 20 A.

k = 0.08 N·m/AIa = 20 A
T = N·m
2.Easy
+−48 VRa​M+−E = 44 Vn = 3000 rpmT

A DC motor turns at 3000 rpm, and its back-EMF at that speed is 44 V. Find the motor constant k in V·s/rad.

E = 44 Vn = 3000 rpm
k = V·s/rad
3.Medium
T (N·m)n (rpm)24 N·mn0​n = ?

A DC motor (k = 0.6 N·m/A, Ra = 0.5 Ω) runs from 220 V and drives a load torque of 24 N·m. Find its speed n in rpm.

V = 220 Vk = 0.6 N·m/ARa = 0.5 ΩT = 24 N·m
n = rpm
4.Medium
+−220 VRa​ = 0.5 ΩIa​ = 50 AM+−EωT

A DC motor draws 50 A from a 220 V supply. Its armature resistance is 0.5 Ω and its rotational (friction, windage and iron) losses are 390 W. Find its efficiency η.

V = 220 VIa = 50 ARa = 0.5 ΩProt = 390 W
η = %
5.Hard
+−240 VD = ?Ra​ = 1 ΩM+−En = 900 rpmT = 37.5 N·m

A DC chopper feeds a motor (k = 1.5 V·s/rad, Ra = 1 Ω) from a 240 V DC bus. The average armature voltage is D·240 V. Find the duty cycle D that runs the motor at 900 rpm with a load of 37.5 N·m.

Vdc = 240 Vk = 1.5 V·s/radRa = 1 ΩT = 37.5 N·mn = 900 rpm
D = %
6.Hard
+−48 VRa​ = 0.8 ΩM+−EωT

A small DC motor has an armature resistance of 0.8 Ω and runs from 48 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 48 VRa = 0.8 Ω
Pmax = W

Answer key

  1. 1. T = 1.6 N·m
  2. 2. k = 0.1401 V·s/rad
  3. 3. n = 3183 rpm
  4. 4. η = 85.09 %
  5. 5. D = 69.32 %
  6. 6. Pmax = 720 W

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