An electric motor converts electrical energy into mechanical work and an electric generator converts mechanical work into electrical energy. The symmetry between the motor and generator naturally leads to questions about creating a perpetual motion machine. The allure of this question has inspired textbook problems, physics education articles, and award-winning physics demonstrations. It is commonly taught that spinning a generator faster produces a larger electromotive force (EMF), because the generator’s instantaneous EMF is proportional to the angular rate of rotation. When making this point in class, students will often ask about an interesting thought experiment, which is depicted in Fig. 1. The student question is as follows: “If an electric motor is connected via a system of gears to an electric generator, so that the generator spins faster than the motor, then does the generator’s output power PG exceed the motor’s input power PM ?”

1.
See for instance Lou A. Bloomfield’s response to a question asked on Physics Central. Available at www.physicscentral.com/experiment/askaphysicist/physics-answer.cfm?uid= 20080506025000.
2.
Kurttscotage
, “
Electric Motor to Motor, can they self run?
” YouTube, https: //www.youtube.com/watch?v=b5NKs-18dK8 (
2014
).
3.
H. D.
Young
,
R. A.
Freedman
, and
A. L.
Ford
,
University Physics with Modern Physics
, 14th ed. (
Pearson
,
London, UK
,
2016
), Question 20.8, p.
676
.
4.
J.
Yap
and
D.
MacIsaac
, “
Analyzing simple electric motors in the classroom
,”
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41
,
427
431
(
Aug.
2006
).
5.
R. J.
Whitaker
, “
Motors and bulbs in series
,”
Phys. Teach.
47
,
353
354
(
Sept.
2009
).
6.
Y.
Kraftmakher
, “
Experiments with a DC motor
,”
Eur. J. Phys.
31
,
863
870
(
June
2010
), .
7.
C. E.
Mungan
, “
Motor demonstration using a hand-cranked Genecon
,”
Phys. Teach.
52
,
422
425
(
Oct.
2014
).
8.
Ref. 3, Question 20.8, pp. 960-962.
9.
L.
Turner
, “
A simple demonstration of back EMF
,”
Phys. Teach.
47
,
513
515
(
Nov.
2009
).
10.
The fact that the back EMF, motor current, and the time-averaged powers are all independent of the value of the parameters N, B, and A is a consequence of the assumed symmetry between the motor and generator and not true in general.
11.
P.
Hewitt
, “
Figuring Physics: Overheating motor
,”
Phys. Teach.
41
,
266
267
(
May
2003
).
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