May 1959 Popular Electronics
[Table of Contents]People old and young enjoy waxing nostalgic about
and learning some of the history of early electronics. Popular Electronics was published from October 1954 through April 1985. All copyrights (if any) are hereby acknowledged.

Here
are a few more electronics conundrums with which to exercise the old noodle. These are puzzlers from a 1959 Popular
Electronics magazine, but at least one of them (#4) will likely prove to be a real stickler unless you have seen
a similar resistor mesh problem before. There are no tube circuits to use as an excuse for not getting them  just
resistors, batteries, switches, meters, a motor, and a couple light bulbs. All four would be fair game to present
to an interviewee to see where he/she stands on basic circuit analysis. (see April
Electronic Sticklers)
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Popular Electronics.
Electronic Sticklers
These four thought twisters are arranged in order of increasing difficulty
1 Happy Snap, having only an s.p.s.t. switch, wanted to turn on a floodlight and a pilot light on
the control board at the same time. Expecting no trouble, he wired his setup as shown. After doublechecking
his connections, he held his breath and inserted the wall plug. Things didn't quite work out. Do you have any
idea why?
Robert L. Noland

2 Dewey Dubblecheck, who believes in making all measurements twice, connected a voltmeter and an
ammeter to measure the power drawn in this circuit. Using the formula: W = E x I, he found that the motor drew
40 watts. He made the measurement again, this time using a standard wattmeter, and read only 30 watts. Dewey
is puzzled  are you?
Donald R. Wesson

3 Sam Addit made this simple computer to add any numbers from 1 to 6. The resistors were adjusted
so that if battery #1 were switched in, the 015 voltmeter would read 1, switching in battery #2 would give
a reading of 2, and so on. He figured that if a combination like 2 and 5 were used, the meter would read 7.
What did it actually read ?
Hal Carlson

4 Ned Work has a mesh of 1ohm resistors connected as shown and extending across his living room
floor. Some day he hopes to extend the mesh all the way to infinity  and maybe even beyond. Can you calculate
what the resistance will be between points "A" and "B" when his "tangled web" is finished?
Roy S. Reichert &
Gene Harris 
Answers to Electronic Sticklers
1. With the switch off, the lights will be in series across 117 volts ±6
volts. Pilot light will pop first, then the floodlight will go out.
2. Dewey failed to consider
power factor when he made his original measurement with a voltmeter and ammeter. The wattmeter automatically took
power factor into consideration. In this circuit the power factor is 0.75.
3. The reading would
be 5 because the batteries are connected in parallel. Actually, unless the resistors are very large in value, the
meter will read some value between 2 and 5 due to the loop current set up in the parallel circuit.
4. Although it is not practical to construct an infinite mesh, you can solve this problem by using a variation
of the constant current method for solving network problems.
Assume that
a battery is connected to the mesh in such a way that one terminal of the battery is connected to point "A" and
the other terminal is connected at infinity. The size and polarity of the battery is such that 1 ampere of current
flows "into the paper" at point "A". Since the three resistors connected to point "A" are all equal (1 ohm) and
the surrounding mesh is symmetrical, the current divides equally in the three branches. Hence, the current in the
resistor between "A" and "B" is 1/3 ampere (i
_{a}).
Now connect a second battery in a similar fashion, only in this case, while one terminal again connects at infinity,
the other terminal is connected to point "B". The size and polarity of this battery is such that 1 ampere of current
flows "out of the paper" at "B". Again, for the same reason, the current divides equally. Hence, an additional 1/3
ampere (i
_{b}) flows through the resistor between "A" and "B" in the same direction
as the current from the first battery. Since one terminal of each battery is connected at infinity, the two currents
at this point are equal and opposite; therefore, they cancel. The infinite extremes of the mesh may be neglected.
It can be seen that a total current through the resistor (i
_{a}
+ i
_{b}) is 2/3 ampere. Since this resistor equals 1 ohm, the voltage drop
across it will be 2/3 volt. It follows then that since 1 ampere of current flows into point "A" and out of point
"B," and the voltage drop from "A" to "B" is 2/3 volt, the total mesh resistance is: R = E/1, or 2/3 volt/1 ampere,
or 2/3 of an ohm.
If you know of a tricky Electronic Stickler, send it
in with the solution to the editors of POPULAR ELECTRONICS. If it is accepted, we will send you a $5 check. Write
each Stickler you would like to submit on the back of a postcard. Submit as many postcards as you like but, please,
just one Stickler per postcard. Send to: POPULAR ELECTRONICS STICKLERS, One Park Ave., New York 16, N. Y. Sorry,
but we will not be able to return unused Sticklers.
Posted
2/7/2013