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​M+−E = 116 Vn = 1800 rpmT

A DC motor turns at 1800 rpm, and its back-EMF at that speed is 116 V. Find the motor constant k in V·s/rad.

E = 116 Vn = 1800 rpm
k = V·s/rad
2.Easy
+−240 VRa​ = 1.2 ΩIa​ = 20 AM+−En = ?T

A DC motor with k = 0.6 V·s/rad and an armature resistance of 1.2 Ω runs from 240 V and draws 20 A. Find its speed n in rpm.

V = 240 VRa = 1.2 ΩIa = 20 Ak = 0.6 V·s/rad
n = rpm
3.Medium
T (N·m)n (rpm)Tst​ = ?n0​

A DC motor with k = 0.2 N·m/A and Ra = 0.8 Ω is connected to 24 V. Find its stall torque Tstall, the torque at zero speed.

V = 24 Vk = 0.2 N·m/ARa = 0.8 Ω
Tstall = N·m
4.Medium
+−240 VRa​ = 0.5 ΩIa​ = 30 AM+−EωT

A DC motor draws 30 A from a 240 V supply. Its armature resistance is 0.5 Ω and its rotational (friction, windage and iron) losses are 540 W. Find its efficiency η.

V = 240 VIa = 30 ARa = 0.5 ΩProt = 540 W
η = %
5.Hard
+−240 VRs​ = ?Ra​ = 1.5 ΩM+−En = 500 rpmT = 12 N·m

A DC motor (k = 0.8 V·s/rad, Ra = 1.5 Ω) on a fixed 240 V supply drives a load of 12 N·m. Find the series resistance Rs that slows it down to 500 rpm.

V = 240 Vk = 0.8 V·s/radRa = 1.5 ΩT = 12 N·mn = 500 rpm
Rs = Ω
6.Hard
+−48 VRa​ = 1.5 ΩM+−EωT

A small DC motor has an armature resistance of 1.5 Ω and runs from 48 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 48 VRa = 1.5 Ω
Pmax = W

Answer key

  1. 1. k = 0.6154 V·s/rad
  2. 2. n = 3438 rpm
  3. 3. Tstall = 6 N·m
  4. 4. η = 86.25 %
  5. 5. Rs = 11.71 Ω
  6. 6. Pmax = 384 W

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