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What's Your EQ?
October 1963 Radio-Electronics

October 1963 Radio-Electronics

October 1963 Radio-Electronics Cover - RF Cafe[Table of Contents]

Wax nostalgic about and learn from the history of early electronics. See articles from Radio-Electronics, published 1930-1988. All copyrights hereby acknowledged.

Here are three new circuit puzzlers in the "What's Your EQ?" (Electronics Quotient) section of the October 1963 Radio-Electronics magazine. All three are as applicable today as they were then, since none involve outdate technology like vacuum tubes. The first one involves a 3-phase motor fed by a 3-Ø, 220 V line source. My answer differs from the creator's in that I assumed maybe the source change was from a 3-Ø wye transformer to a 3-Ø delta transformer, thus depriving the photocell circuit local step-down transformer of a true ground-referenced neutral point, as a wye has. In a wye line supply for 3-Ø, 220 V, the potential between any phase and neutral/ground is 220/√3 = 127 V. That is close enough to the rated 120 V to not cause a problem. However, a 3-Ø delta transformer has no direct neutral / ground reference, so feeding a 220 V phase to the local transformer, into the 110 V tap would overdrive the transformer, causing it to possibly overheat, and definitely output too high of a voltage for the photocell circuit. My answer is ultimately correct regarding why the system failed in then new location, and the puzzler creator never mentions why it might have been OK in its original location (where my suggestion is probably correct). The other two are routine circuit analysis problems.

What's Your EQ?

What's Your EQ?, October 1963 Radio-Electronics - RF CafeThree puzzlers for the student, theoretician and practical man. Simple? Double-check your answers before you say you've solved them. If you have on interesting or unusual puzzle (with an answer!) send it to us, We will pay $10 for each one accepted. We're especially interested in service stinkers or engineering stumpers on actual electronic equipment. We get so many letters we can't answer individual ones, but we'll print the more interesting solutions - ones the original authors never thought of.

Write EQ Editor, Radio-Electronics, 154 West 14th Street, New York, N. Y. 10011.

Answers to this month's puzzles are on page 72.

Power Supply Puzzler - RF CafePower Supply Puzzler

The photocell controller for a factory conveyor refused to work after reinstallation in a new spot. It was supposed to stop the conveyor motor when a box broke the beam. A 3-phase 220-volt line supplied power to the motor. The power transformer of the photocell relay control amplifier, a standard 110-220-volt tapped transformer, was connected between the center leg of the 220-volt line and ground. The transformer overheated and resistors burned up. When the tap was moved to 220 volts, the amplifier still refused to work.

The complete system was taken to the shop. There, it worked perfectly on both 110- and 220-volt supply, yet it refused to work on the machine. What's the matter? Possible hint for solution:

"Industrial Electrician" employed by local factory was kid who actually didn't know what three-phase current is. Argued for three days, despite actual demonstrations on nearby power supply. He got the motor to work by following wire colors, but couldn't get the photo-cell amplifier to work at all.

- J. Darr

 

Output Voltage Puzzler - RF CafeOutput Voltage

What is the output voltage across the bridge? Can you prove it mathematically?

- Cameron McCulloch

 

Double Grid Puzzler - RF CafeDouble Grid

All resistors are equal and the total current is 1 ampere. What is the value of each resistor?

- Kendall Collins

Quizzes from vintage electronics magazines such as Popular Electronics, Electronics-World, QST, Radio-Electronics, and Radio News were published over the years - some really simple and others not so simple. Robert P. Balin created most of the quizzes for Popular Electronics. This is a listing of all I have posted thus far.

RF Cafe Quizzes

Vintage Electronics Magazine Quizzes

Vintage Electronics Magazine Quizzes

Vintage Electronics Magazine Quizzes

Answers to What's Your Eq?

These are the answers.

Puzzles on page 39.

Power Supply Puzzler

Wrong primary power supply! You can not get "110 volts" or "220 volts", single-phase, by tapping into a three-phase 220-volt supply line! The voltage read between the center leg and ground actually comes out something like 165 volts or more, depending upon how good the ground is! This is due to the waveform of the voltage; the actual average voltage between any wire and earth ground is far above a single-phase average! Came out something like 165 or 175 volts, which, of course, burned up resistors in the photocell amplifier. Solution: Run a single-phase 110-volt line from a nearby lighting circuit to the amplifier, which then worked perfectly.

 

Output Voltage Solution - RF CafeOutput Voltage

The ratio of output voltage (as measured with a vtvm) to input voltage is always 1/2 - for any frequency including dc, any value of C or any value of R! The only requirement is that the two resistors marked r be equal.

Proof? Here goes. (See the diagram.) For convenience, let's call the input voltage 2E (we can call it any-thing we like, after all). Since r = r, the voltage at A (VA) must be 1/2(2E), or just E. By the same voltage-divider reasoning, the voltage at B (VB) will be

VB = 2E(R/(R - jXC),

where jXC is C's reactance. Now we know VA and VB (at least in symbols). The output voltage V must be the difference between them: V = VA - VB. Substituting our expressions for VA and VB, we get

Voltage equation - RF Cafe 

But the absolute value (magnitude) of the expression in parentheses is just 1 (unity), hence V = E, or exactly half the input. Note that the proof contains no f's or omegas - the voltage does not depend on frequency - and also that the R's and X's drop out. Thus the solution holds, as we said, for any value of f, C or R.

 

Double Grid

This is simply the old cube circuit, presented in an unconventional way. Each resistor is 6 ohms. An equivalent circuit is shown for convenience in analyzing the cube circuit. The voltages at a, b and c are identical, as are those at d, e and f. Therefore, they can be shown connected together for purposes of calculation. Then, if the effective resistance of the circuit is 5 ohms (5 volts/1 amp) the value of anyone resistor in the circuit can be found:

R = I network resistor

5 ohms = 1/3 R + 1/6 R + 1/3 R

5 ohms = 5/6 R

R = 6 ohms. 
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About RF Cafe

Kirt Blattenberger - RF Cafe Webmaster

Copyright: 1996 - 2025
Webmaster: Kirt Blattenberger,
   BSEE - KB3UON - AMA92498

RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The World Wide Web (Internet) was largely an unknown entity at the time and bandwidth was a scarce commodity. Dial-up modems blazed along at 14.4 kbps while tying up your telephone line, and a lady's voice announced "You've Got Mail" when a new message arrived...

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