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
+−240 VRa​M+−E = 225 Vn = 3000 rpmT

A DC motor turns at 3000 rpm, and its back-EMF at that speed is 225 V. Find the motor constant k in V·s/rad.

E = 225 Vn = 3000 rpm
k = V·s/rad
2.Easy
+−24 VRa​Ia​ = 4 AM+−EωT = ?

A permanent-magnet DC motor has the torque constant k = 1.2 N·m/A. Find the torque T it develops at an armature current of 4 A.

k = 1.2 N·m/AIa = 4 A
T = N·m
3.Medium
T (N·m)n (rpm)n0​ = ?

A DC motor with k = 1 V·s/rad runs from 220 V. Neglecting all losses at no load, find its no-load speed n0 in rpm.

V = 220 Vk = 1 V·s/rad
n0 = rpm
4.Medium
+−VRa​M+−En = 2000 rpmT = ?

A DC motor delivers 1 kW of mechanical power at 2000 rpm. Find the shaft torque T.

P = 1 kWn = 2000 rpm
T = N·m
5.Hard
+−110 VRa​ = 0.8 ΩM+−EωT

A small DC motor has an armature resistance of 0.8 Ω and runs from 110 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 110 VRa = 0.8 Ω
Pmax = W
6.Hard
+−48 VD = ?Ra​ = 0.4 ΩM+−En = 600 rpmT = 0.6 N·m

A DC chopper feeds a motor (k = 0.1 V·s/rad, Ra = 0.4 Ω) from a 48 V DC bus. The average armature voltage is D·48 V. Find the duty cycle D that runs the motor at 600 rpm with a load of 0.6 N·m.

Vdc = 48 Vk = 0.1 V·s/radRa = 0.4 ΩT = 0.6 N·mn = 600 rpm
D = %

Answer key

  1. 1. k = 0.7162 V·s/rad
  2. 2. T = 4.8 N·m
  3. 3. n0 = 2101 rpm
  4. 4. T = 4.775 N·m
  5. 5. Pmax = 3781 W
  6. 6. D = 18.09 %

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