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​M+−E = 42 Vn = 1000 rpmT

A DC motor turns at 1000 rpm, and its back-EMF at that speed is 42 V. Find the motor constant k in V·s/rad.

E = 42 Vn = 1000 rpm
k = V·s/rad
2.Easy
+−220 VRa​ = 0.4 ΩIa​ = 50 AM+−EωT

A DC motor runs from 220 V with an armature current of 50 A. The armature resistance is 0.4 Ω. Find the developed (electromagnetic) power Pdev.

V = 220 VIa = 50 ARa = 0.4 Ω
Pdev = W
3.Medium
T (N·m)n (rpm)4 N·mn0​nFL​

A DC motor (k = 1 V·s/rad, Ra = 2 Ω) runs from 240 V. At full load it draws 4 A. Neglecting the no-load current, find its speed regulation SR = (n₀ − nFL)/nFL in percent.

V = 240 Vk = 1 V·s/radRa = 2 ΩIFL = 4 A
SR = %
4.Medium
T (N·m)n (rpm)48 N·mn0​n = ?

A DC motor (k = 1.2 N·m/A, Ra = 0.2 Ω) runs from 120 V and drives a load torque of 48 N·m. Find its speed n in rpm.

V = 120 Vk = 1.2 N·m/ARa = 0.2 ΩT = 48 N·m
n = rpm
5.Hard
+−220 VRs​ = ?Ra​ = 1.2 ΩM+−En = 500 rpmT = 12 N·m

A DC motor (k = 0.8 V·s/rad, Ra = 1.2 Ω) on a fixed 220 V supply drives a load of 12 N·m. Find the series resistance Rs that slows it down to 500 rpm.

V = 220 Vk = 0.8 V·s/radRa = 1.2 ΩT = 12 N·mn = 500 rpm
Rs = Ω
6.Hard
+−48 VRa​ = 2.5 ΩM+−EωT

A small DC motor has an armature resistance of 2.5 Ω and runs from 48 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 48 VRa = 2.5 Ω
Pmax = W

Answer key

  1. 1. k = 0.4011 V·s/rad
  2. 2. Pdev = 10000 W
  3. 3. SR = 3.448 %
  4. 4. n = 891.3 rpm
  5. 5. Rs = 10.67 Ω
  6. 6. Pmax = 230.4 W

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