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
+−48 VRa​ = 0.25 ΩIa​ = ?M+−E = 46.5 VωT

A DC motor on a 48 V supply has an armature resistance of 0.25 Ω. At its present speed the back-EMF is 46.5 V. Find the armature current Ia.

V = 48 VE = 46.5 VRa = 0.25 Ω
Ia = A
2.Easy
+−220 VRa​ = 0.5 ΩIa​ = ?M+−E = 210 VωT

A DC motor on a 220 V supply has an armature resistance of 0.5 Ω. At its present speed the back-EMF is 210 V. Find the armature current Ia.

V = 220 VE = 210 VRa = 0.5 Ω
Ia = A
3.Medium
+−240 VRa​ = 1.2 ΩIa​ = 12 AM+−EωT

A DC motor draws 12 A from a 240 V supply. Its armature resistance is 1.2 Ω and its rotational (friction, windage and iron) losses are 162 W. Find its efficiency η.

V = 240 VIa = 12 ARa = 1.2 ΩProt = 162 W
η = %
4.Medium
T (N·m)n (rpm)n0​ = ?

A DC motor with k = 0.75 V·s/rad runs from 240 V. Neglecting all losses at no load, find its no-load speed n0 in rpm.

V = 240 Vk = 0.75 V·s/rad
n0 = rpm
5.Hard
+−48 VRa​ = 0.8 ΩIa​: 6 → 9 AM+−En = ?T

A separately excited DC motor on 48 V (Ra = 0.8 Ω) runs at 1200 rpm with an armature current of 6 A. The load changes and the current becomes 9 A, with the field unchanged. Find the new speed n2.

V = 48 VRa = 0.8 Ωn1 = 1200 rpmIa1 = 6 AIa2 = 9 A
n2 = rpm
6.Hard
+−240 VD = ?Ra​ = 1.5 ΩM+−En = 1000 rpmT = 7.2 N·m

A DC chopper feeds a motor (k = 1.2 V·s/rad, Ra = 1.5 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 1000 rpm with a load of 7.2 N·m.

Vdc = 240 Vk = 1.2 V·s/radRa = 1.5 ΩT = 7.2 N·mn = 1000 rpm
D = %

Answer key

  1. 1. Ia = 6 A
  2. 2. Ia = 20 A
  3. 3. η = 88.37 %
  4. 4. n0 = 3056 rpm
  5. 5. n2 = 1133 rpm
  6. 6. D = 56.11 %

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