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
+−110 VRa​M+−E = 106 Vn = 3000 rpmT

A DC motor turns at 3000 rpm, and its back-EMF at that speed is 106 V. Find the motor constant k in V·s/rad.

E = 106 Vn = 3000 rpm
k = V·s/rad
2.Easy
+−240 VRa​ = 0.8 ΩIa​ = 15 AM+−E = ?ωT

A DC motor runs from a 240 V supply and draws an armature current of 15 A. Its armature resistance is 0.8 Ω. Find the back-EMF E.

V = 240 VIa = 15 ARa = 0.8 Ω
E = V
3.Medium
T (N·m)n (rpm)15 N·mn0​n = ?

A DC motor (k = 0.75 N·m/A, Ra = 0.4 Ω) runs from 110 V and drives a load torque of 15 N·m. Find its speed n in rpm.

V = 110 Vk = 0.75 N·m/ARa = 0.4 ΩT = 15 N·m
n = rpm
4.Medium
T (N·m)n (rpm)0.16 N·mn0​n = ?

A DC motor (k = 0.08 N·m/A, Ra = 1.2 Ω) runs from 24 V and drives a load torque of 0.16 N·m. Find its speed n in rpm.

V = 24 Vk = 0.08 N·m/ARa = 1.2 ΩT = 0.16 N·m
n = rpm
5.Hard
T (N·m)n (rpm)15 N·m1500 rpm

A DC motor with k = 0.75 V·s/rad and Ra = 0.8 Ω must drive a load of 15 N·m at 1500 rpm. Find the armature voltage V it needs.

k = 0.75 V·s/radRa = 0.8 ΩT = 15 N·mn = 1500 rpm
V = V
6.Hard
+−120 VRa​ = 1.5 ΩIa​: 4 → 6 AM+−En = ?T

A separately excited DC motor on 120 V (Ra = 1.5 Ω) runs at 1000 rpm with an armature current of 4 A. The load changes and the current becomes 6 A, with the field unchanged. Find the new speed n2.

V = 120 VRa = 1.5 Ωn1 = 1000 rpmIa1 = 4 AIa2 = 6 A
n2 = rpm

Answer key

  1. 1. k = 0.3374 V·s/rad
  2. 2. E = 228 V
  3. 3. n = 1299 rpm
  4. 4. n = 2578 rpm
  5. 5. V = 133.8 V
  6. 6. n2 = 973.7 rpm

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