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​ = 1.5 ΩIa​ = 6 AM+−E = ?ωT

A DC motor runs from a 120 V supply and draws an armature current of 6 A. Its armature resistance is 1.5 Ω. Find the back-EMF E.

V = 120 VIa = 6 ARa = 1.5 Ω
E = V
2.Easy
+−220 VRa​ = 0.4 ΩIa​ = ?M+−E = 0n = 0T

A DC motor with an armature resistance of 0.4 Ω is switched directly onto a 220 V supply. Its normal full-load current is 40 A. Find the armature current Istart at the moment of starting.

V = 220 VRa = 0.4 Ω
Istart = A
3.Medium
T (N·m)n (rpm)30 N·mn0​n = ?

A DC motor (k = 1 N·m/A, Ra = 0.2 Ω) runs from 120 V and drives a load torque of 30 N·m. Find its speed n in rpm.

V = 120 Vk = 1 N·m/ARa = 0.2 ΩT = 30 N·m
n = rpm
4.Medium
+−110 VRa​ = 0.25 ΩIa​ = 50 AM+−EωT

A DC motor draws 50 A from a 110 V supply. Its armature resistance is 0.25 Ω and its rotational (friction, windage and iron) losses are 244 W. Find its efficiency η.

V = 110 VIa = 50 ARa = 0.25 ΩProt = 244 W
η = %
5.Hard
+−240 VRs​ = ?Ra​ = 1.5 ΩM+−En = 300 rpmT = 30 N·m

A DC motor (k = 2 V·s/rad, Ra = 1.5 Ω) on a fixed 240 V supply drives a load of 30 N·m. Find the series resistance Rs that slows it down to 300 rpm.

V = 240 Vk = 2 V·s/radRa = 1.5 ΩT = 30 N·mn = 300 rpm
Rs = Ω
6.Hard
+−240 VRs​ = ?Ra​ = 2 ΩM+−En = 500 rpmT = 7.5 N·m

A DC motor (k = 1.5 V·s/rad, Ra = 2 Ω) on a fixed 240 V supply drives a load of 7.5 N·m. Find the series resistance Rs that slows it down to 500 rpm.

V = 240 Vk = 1.5 V·s/radRa = 2 ΩT = 7.5 N·mn = 500 rpm
Rs = Ω

Answer key

  1. 1. E = 111 V
  2. 2. Istart = 550 A
  3. 3. n = 1089 rpm
  4. 4. η = 84.2 %
  5. 5. Rs = 10.31 Ω
  6. 6. Rs = 30.29 Ω

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