# Two random theory questions

#### poopscoop

Joined Dec 12, 2012
140
1. From my understanding of an alternator, specifically an automobile style alternator with an energized rotor(?), varying the energy (voltage or current?) to the rotor allows you to control the output of the alternator, thereby controlling voltage. When load increases the control assembly increases energy in the rotor, which thus increases overall alternator output and allows the system to maintain voltage over varying levels of load. Assuming there were no battery in the car, if the the load on the alternator suddenly increased (Say the lights were turned on), would the alternator be able to increase output to compensate for the load? If there is no reserve supply of power to increase energy to the rotor, how can the alternator compensate for an increase in load?

2. How does a home in the US, fed with 120vac/60hz single phase, provide 208v to dryers/water heaters/etc? I understand how it does from polyphase systems, but how is it done on single phase?

Random questions, yes, but these things puzzle me.

#### WBahn

Joined Mar 31, 2012
29,150
1. From my understanding of an alternator, specifically an automobile style alternator with an energized rotor(?), varying the energy (voltage or current?) to the rotor allows you to control the output of the alternator, thereby controlling voltage. When load increases the control assembly increases energy in the rotor, which thus increases overall alternator output and allows the system to maintain voltage over varying levels of load. Assuming there were no battery in the car, if the the load on the alternator suddenly increased (Say the lights were turned on), would the alternator be able to increase output to compensate for the load? If there is no reserve supply of power to increase energy to the rotor, how can the alternator compensate for an increase in load?
The specific answer depends on some details about car alternator design that I don't know, but in general if your generator/alternator uses electromagnets then you have to have some means of bootstrapping the system to get it going. Once going, it can be designed to bleed energy from the output to provide power for the electromagnets.

2. How does a home in the US, fed with 120vac/60hz single phase, provide 208v to dryers/water heaters/etc? I understand how it does from polyphase systems, but how is it done on single phase?
A home in the U.S. does not provide 208VAC to those appliances, it provides 240VAC to them. I suspect that is enough for you to answer your own question, but for the benefit of others, each house is supplied with two hot lines, drawn from a 240VAC transformer, along with a third center-tapped line called the neutral. The 120VAC circuits in the house are organized so that half or from one hot line to the neutral and the other half are from the other hot line to the neutral. The high voltage loads are powered between the two hot lines.

#### crutschow

Joined Mar 14, 2008
32,850
Their may be enough residual magnetism in the alternator rotor to give a small output voltage. This can then provide some extra current to the rotor windings to increase the voltage further, bootstrapping itself until it reaches its operating output voltage.

#### poopscoop

Joined Dec 12, 2012
140
A home in the U.S. does not provide 208VAC to those appliances, it provides 240VAC to them. I suspect that is enough for you to answer your own question, but for the benefit of others, each house is supplied with two hot lines, drawn from a 240VAC transformer, along with a third center-tapped line called the neutral. The 120VAC circuits in the house are organized so that half or from one hot line to the neutral and the other half are from the other hot line to the neutral. The high voltage loads are powered between the two hot lines.
So, since every neighborhood I've seen is fed by single phase, the transformer puts out two separate sine waves, 180* offset? Each line is obviously 120vac WRT ground/neutral, but 240vac WRT each other?

#### WBahn

Joined Mar 31, 2012
29,150
So, since every neighborhood I've seen is fed by single phase, the transformer puts out two separate sine waves, 180* offset? Each line is obviously 120vac WRT ground/neutral, but 240vac WRT each other?
Yes and no. Probably the most accurate way to think of it is a single-phase transformer that is putting out 240VAC and that happens to also be center tapped. If you take two lines that have a sinusoidal voltage difference between them and then compute the voltage difference between the average voltage between them (the center tap) and either of the two lines, you will end up with two sinusoids of half the amplitude that are 180 degrees out of phase.

Va = voltage on line A
Vb = Va+Asin(wt) = voltage on line A
Vn = (Va + Vb)/2 = voltage on the center tapped "neutral"

Calculate

First note that

Vba = Vb - Va = Asin(wt) = voltage from line B to line A

Van = voltage from line A to the neutral
Vbn = voltage from line B to the neutral

Van = Va - Vn
= Va - (Va+Vb)/2
= (Va - Vb)/2
= -(Vb - Va)/2
= -Asin(wt)/2

Vbn = Vb - Vn
= Vb - (Va + Vb)/2
= (Vb - Va)/2
= Asin(wt)/2

Also, you'll see it called 220V, 230V, or 240V -- my understanding is that the 220V is an old designation, the 230V comes from product design standards, and 240V is the nominal voltageactually delivered at the transformer.