Transformers (G5C06)

The 2019-2023 General License question pool includes questions about the function of electrical transformers:

G5C06: What is the RMS voltage across a 500-turn secondary winding in a transformer if the 2250-turn primary is connected to 120 VAC?

A. 2370 volts

B. 540 volts

C. 26.7 volts

D. 5.9 volts

Transformer Bumblebee, courtesy Paramount Pictures.

Transformers! Wow, those guys are really cool with all their giant robotic changes back and forth to 18-wheeler rigs or colorful sports cars! Who knew we’d get to study transformers for our ham radio license? How exciting!

Unfortunately, this question is referring to a slightly more mundane type of transformer that doesn’t usually change its physical form very much unless it receives a glancing lightning strike and associated surge currents. But this type of transformer does something almost as amazing as the movie type…

An inductor stores energy in a magnetic field. The magnetic field reverses the direction of its field lines with reversals in direction of AC.

It transforms AC voltage from one value to another! Fantastic!

How, you now ask, does a real life transformer perform this amazing task? It uses the concept of mutual inductance. Inductance, you will recall, is the storage of energy in a magnetic field, usually accomplished by sending current through a coil of wire. The magnetic field inflates about the inductive coil as current flows in one direction, and when AC reverses direction the field is deflated and re-inflated with opposite polarity lines of magnetic force. Mutual inductance occurs when two nearby coils affect one another with the induced magnetic field. Let’s consider the transformer case of this.

With mutual inductance in a transformer, two coils share a common core (frequently iron). That is, two different wires are wrapped in coils around the same hunk of metal. When AC is applied to one of the wire coils (the “primary winding”) an inflating-deflating-inflating magnetic field is created about that energized coil. By some really swanky rules of electromagnetic physics, when a magnetic field moves or changes near a conductor, an electric current is induced in that conductor. So, as our electrically energized primary winding is doing its magnetic dance, the other wire coil (the “secondary winding”) isn’t just standing against the wall waiting for an invitation onto the dance floor. It senses the rapidly changing magnetic field and, like a teenage funk junkie that just can’t fight the beat, the secondary winding begins pulsing with back and forth electrical current that we call AC. This is a result of mutual inductance. However…

Depending upon the construction of the transformer, the value of the voltage that is induced in the secondary winding will be different from the voltage in the externally energized primary winding. The relationship can be easily calculated using ratios. Specifically, the ratio of the voltages of the two wire windings on the transformer must be equal to the ratio of the number of windings. So, if the secondary winding has 1/10 as many loops as the primary winding, the voltage induced in the secondary winding will be 1/10 the voltage energizing the primary. Here is the simple equation relating these ratios:

Es/Ep = Ns/Np

A transformer with primary and secondary windings as described in this question item.

…where Es is the voltage of the secondary and Ep is the voltage of the primary; Ns is the number of windings of the secondary and Np is the number of windings of the primary.

Using a smidgeon of algebraic magic we can solve for Es like this:

Es = Ep x Ns/Np

“Aha!” you now exclaim, as if you just realized why your shiny new yellow and black Camaro was acting so strangely. Instead, you simply realized how to answer question G5C06. You begin to plug in the question’s numbers to the equation above and, like Optimus Prime, its generic symbols are transformed into a specific solution.

Es = 120v x 500/2250

Es = 120v x 0.222

Es = 26.7 V

Now, as an afterthought, what about that “RMS voltage” term in the question? No worries. AC voltage values are expressed as RMS values, so this may be ignored. The term means root mean square, and it is computed as 0.707 x peak voltage of a sine wave AC signal. RMS voltage is explained in the General License Course book section 6.1, Power & Principles, but that’s question for another article.

The answer to General Class question G5C06, “What is the RMS voltage across a 500-turn secondary winding in a transformer if the 2250-turn primary is connected to 120 VAC?”is “C. 26.7 volts.”

-- Stu WØSTU