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
+−220 VRa​M+−E = 190 Vn = 2000 rpmT

A DC motor turns at 2000 rpm, and its back-EMF at that speed is 190 V. Find the motor constant k in V·s/rad.

E = 190 Vn = 2000 rpm
k = V·s/rad
2.Easy
+−48 VRa​ = 0.25 ΩIa​ = 15 AM+−En = ?T

A DC motor with k = 0.5 V·s/rad and an armature resistance of 0.25 Ω runs from 48 V and draws 15 A. Find its speed n in rpm.

V = 48 VRa = 0.25 ΩIa = 15 Ak = 0.5 V·s/rad
n = rpm
3.Medium
+−VRa​M+−En = 1000 rpmT = ?

A DC motor delivers 0.75 kW of mechanical power at 1000 rpm. Find the shaft torque T.

P = 0.75 kWn = 1000 rpm
T = N·m
4.Medium
T (N·m)n (rpm)22.5 N·mn0​n = ?

A DC motor (k = 0.75 N·m/A, Ra = 1 Ω) runs from 240 V and drives a load torque of 22.5 N·m. Find its speed n in rpm.

V = 240 Vk = 0.75 N·m/ARa = 1 ΩT = 22.5 N·m
n = rpm
5.Hard
+−120 VRa​ = 2.5 ΩM+−EωT

A small DC motor has an armature resistance of 2.5 Ω and runs from 120 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 120 VRa = 2.5 Ω
Pmax = W
6.Hard
+−240 VD = ?Ra​ = 0.8 ΩM+−En = 300 rpmT = 50 N·m

A DC chopper feeds a motor (k = 2 V·s/rad, Ra = 0.8 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 300 rpm with a load of 50 N·m.

Vdc = 240 Vk = 2 V·s/radRa = 0.8 ΩT = 50 N·mn = 300 rpm
D = %

Answer key

  1. 1. k = 0.9072 V·s/rad
  2. 2. n = 845.1 rpm
  3. 3. T = 7.162 N·m
  4. 4. n = 2674 rpm
  5. 5. Pmax = 1440 W
  6. 6. D = 34.51 %

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