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
+−120 VRa​ = 0.25 ΩIa​ = ?M+−E = 116.3 VωT

A DC motor on a 120 V supply has an armature resistance of 0.25 Ω. At its present speed the back-EMF is 116.3 V. Find the armature current Ia.

V = 120 VE = 116.3 VRa = 0.25 Ω
Ia = A
2.Easy
+−120 VRa​Ia​ = 30 AM+−EωT = ?

A permanent-magnet DC motor has the torque constant k = 1.2 N·m/A. Find the torque T it develops at an armature current of 30 A.

k = 1.2 N·m/AIa = 30 A
T = N·m
3.Medium
T (N·m)n (rpm)0.6 N·mn0​n = ?

A DC motor (k = 0.15 N·m/A, Ra = 0.5 Ω) runs from 48 V and drives a load torque of 0.6 N·m. Find its speed n in rpm.

V = 48 Vk = 0.15 N·m/ARa = 0.5 ΩT = 0.6 N·m
n = rpm
4.Medium
+−24 VRa​ = 0.25 ΩIa​ = 6 AM+−EωT

A DC motor draws 6 A from a 24 V supply. Its armature resistance is 0.25 Ω and its rotational (friction, windage and iron) losses are 7 W. Find its efficiency η.

V = 24 VIa = 6 ARa = 0.25 ΩProt = 7 W
η = %
5.Hard
+−120 VD = ?Ra​ = 1.5 ΩM+−En = 600 rpmT = 3.2 N·m

A DC chopper feeds a motor (k = 0.8 V·s/rad, Ra = 1.5 Ω) from a 120 V DC bus. The average armature voltage is D·120 V. Find the duty cycle D that runs the motor at 600 rpm with a load of 3.2 N·m.

Vdc = 120 Vk = 0.8 V·s/radRa = 1.5 ΩT = 3.2 N·mn = 600 rpm
D = %
6.Hard
+−48 VRst​ = ?Ra​ = 0.25 Ω50 AM+−E = 0n = 0T

A 48 V DC motor has an armature resistance of 0.25 Ω. Find the series starting resistance Rst that limits the starting current to 50 A.

V = 48 VRa = 0.25 ΩImax = 50 A
Rst = Ω

Answer key

  1. 1. Ia = 15 A
  2. 2. T = 36 N·m
  3. 3. n = 2928 rpm
  4. 4. η = 88.89 %
  5. 5. D = 46.89 %
  6. 6. Rst = 0.71 Ω

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