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​ = 0.5 ΩIa​ = ?M+−E = 110 VωT

A DC motor on a 120 V supply has an armature resistance of 0.5 Ω. At its present speed the back-EMF is 110 V. Find the armature current Ia.

V = 120 VE = 110 VRa = 0.5 Ω
Ia = A
2.Easy
+−220 VRa​ = 1.2 ΩIa​ = 12 AM+−En = ?T

A DC motor with k = 0.75 V·s/rad and an armature resistance of 1.2 Ω runs from 220 V and draws 12 A. Find its speed n in rpm.

V = 220 VRa = 1.2 ΩIa = 12 Ak = 0.75 V·s/rad
n = rpm
3.Medium
+−220 VRa​ = 0.4 ΩIa​ = 20 AM+−EωT

A DC motor draws 20 A from a 220 V supply. Its armature resistance is 0.4 Ω and its rotational (friction, windage and iron) losses are 127 W. Find its efficiency η.

V = 220 VIa = 20 ARa = 0.4 ΩProt = 127 W
η = %
4.Medium
+−VRa​M+−En = 3000 rpmT = ?

A DC motor delivers 0.5 kW of mechanical power at 3000 rpm. Find the shaft torque T.

P = 0.5 kWn = 3000 rpm
T = N·m
5.Hard
+−240 VD = ?Ra​ = 0.4 ΩM+−En = 900 rpmT = 0.6 N·m

A DC chopper feeds a motor (k = 0.12 V·s/rad, Ra = 0.4 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 0.6 N·m.

Vdc = 240 Vk = 0.12 V·s/radRa = 0.4 ΩT = 0.6 N·mn = 900 rpm
D = %
6.Hard
+−120 VRa​ = 2 ΩM+−EωT

A small DC motor has an armature resistance of 2 Ω and runs from 120 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 120 VRa = 2 Ω
Pmax = W

Answer key

  1. 1. Ia = 20 A
  2. 2. n = 2618 rpm
  3. 3. η = 93.48 %
  4. 4. T = 1.592 N·m
  5. 5. D = 5.546 %
  6. 6. Pmax = 1800 W

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