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 = 216 Vn = 900 rpmT

A DC motor turns at 900 rpm, and its back-EMF at that speed is 216 V. Find the motor constant k in V·s/rad.

E = 216 Vn = 900 rpm
k = V·s/rad
2.Easy
+−48 VRa​ = 1 ΩIa​ = 6 AM+−E = ?ωT

A DC motor runs from a 48 V supply and draws an armature current of 6 A. Its armature resistance is 1 Ω. Find the back-EMF E.

V = 48 VIa = 6 ARa = 1 Ω
E = V
3.Medium
T (N·m)n (rpm)1 N·mn0​n = ?

A DC motor (k = 0.25 N·m/A, Ra = 1.2 Ω) runs from 48 V and drives a load torque of 1 N·m. Find its speed n in rpm.

V = 48 Vk = 0.25 N·m/ARa = 1.2 ΩT = 1 N·m
n = rpm
4.Medium
T (N·m)n (rpm)Tst​ = ?n0​

A DC motor with k = 2 N·m/A and Ra = 0.4 Ω is connected to 240 V. Find its stall torque Tstall, the torque at zero speed.

V = 240 Vk = 2 N·m/ARa = 0.4 Ω
Tstall = N·m
5.Hard
+−48 VRs​ = ?Ra​ = 1.5 ΩM+−En = 300 rpmT = 0.6 N·m

A DC motor (k = 0.3 V·s/rad, Ra = 1.5 Ω) on a fixed 48 V supply drives a load of 0.6 N·m. Find the series resistance Rs that slows it down to 300 rpm.

V = 48 Vk = 0.3 V·s/radRa = 1.5 ΩT = 0.6 N·mn = 300 rpm
Rs = Ω
6.Hard
+−110 VRa​ = 0.8 ΩIa​: 15 → 7.5 AM+−En = ?T

A separately excited DC motor on 110 V (Ra = 0.8 Ω) runs at 1500 rpm with an armature current of 15 A. The load changes and the current becomes 7.5 A, with the field unchanged. Find the new speed n2.

V = 110 VRa = 0.8 Ωn1 = 1500 rpmIa1 = 15 AIa2 = 7.5 A
n2 = rpm

Answer key

  1. 1. k = 2.292 V·s/rad
  2. 2. E = 42 V
  3. 3. n = 1650 rpm
  4. 4. Tstall = 1200 N·m
  5. 5. Rs = 17.79 Ω
  6. 6. n2 = 1592 rpm

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