# Connect motor in 220 VAC single phase (Line - Neutral) or in 110VAC two phases (110VAC - 110VAC "180 degree out of phase")?

I need to connect A motor of 220VAC to single phase connection :Line - Neutral(220VAC - Neutral).

In my country that doesn't exist so in my country we have this : L1-L2-neutral (110VAC - 110VAC "180 degre out of phase" - Neutral).

I would like prove that doesn't matter the way I connect the motor , either Line - Neutral (220VAC - Neutral) or Line1 -Line2 (110VAC - 110VAC "180 degree out of phase" ) .

The following image explain what I try to prove :

So I begin :

Single Phase Connection :

$$Line1 = 220sen(w+\theta)\\ w = 2\pi f; \theta=0\\ w = 2\pi 60H ;\theta=0\\ w= 377rad/s$$

So potential difference in original single phase instalation would be : $$V=220sen(377rad/s)VAC - 0VAC\\ V=220sen(377rad/s)VAC$$

Now in two phases connection:

$$Line1 = 110sen(w+\theta)\\ w = 2\pi f; \theta=0\\ w = 2\pi 60H ;\theta=0\\ w= 377rad/s\\ Line1=110sen(377rad/s)VAC$$

Line two has 180 degree out of phase:

$$Line2=110sen(377-180)\\$$

By trigonometric Identity:

$$L2=110[sen(377)cos(180)-cos(377)sen(180)]\\ L2 = 110[sen(377)*(-1)-0]\\ L2 = -110sen(377rad/s)$$

Finally we do the difference potential of the two Lines in the two phase conection:

$$V =L1 - L2\\$$ $$V=110sen(377rad/seg) -(-110sen(377rad/seg)\\ = 110[sen(377)+sen(377)\\$$ By trigonometric identity:

$$110[2*sen(\frac{377+377}{2}*cos\frac{377-377}{2})]\\$$ Solving we get the two phase difference potential:

$$V=220sen(377rad/s)$$

Voltage in motor in single phase connection is the same that voltage in two phase connection.

So, We say it doesn't matter If I connect the motor in this way (220VAC - Neutral) or this way (110VAC -110VAC) and this mathematical demostration prove that.

Am I wrong ? Or Am I perfect in that demostration ?

• Have you, for Line 2, subtracted 180 rads/s instead of $\pi$ rads/s? Mar 29 '21 at 0:26
• Why are you trying to prove that 110V + 110V= 220V? In North America that is how a stove and clothes dryer are connected. Mar 29 '21 at 0:44
• @Transistor you are right.$180 rad/s$ doesn't make sense
– NIN
Mar 29 '21 at 1:01
• @Audioguru you are right. That's why I try to see it mathematicaly. So you say that 110V +110V is how is connect a clothes dryer. .. But If I connect 220V + Neutral (rather than 110 + 110) it will work , right ?
– NIN
Mar 29 '21 at 1:04
• @NIN If your country has an L1 that is 180 degrees out of phase with L2, referenced to neutral then you have a very common "split phase" system and you can use L1 and L2 for 220 V single phase uses. You are way over thinking this, I fear. But if you need to be absolutely sure, tell us where you live or reference where you are getting your information on your mains so we can look and interpret for you.
– jonk
Mar 29 '21 at 6:22

In a 120V system there isn’t a way to connect 240V to neutral. Each leg is only 120V to neutral. You would instead connect the 240V motor across two ‘hot’ legs at 240V.

In a 120V-market dryer, they sometimes will use a split feed: 120V from one hot to neutral for the motor, and 240V for across the two hot leads for the heater. This allows a gas dryer (which only needs motor power) and an electric to use the same motor, with only the heater being different.

• thank you . . . Let's suppose we have a motor which must be connected in this way : L1 = 120 VAC ; L2 = 120VAC (180 degree out of phase) ; N = Neutral. . . . But I live in a country which I just have two wires : 240VAC and neutral. . You say there isn't a way that motor work ?
– NIN
Mar 29 '21 at 2:18
• Nope. You need a 240V motor. There isn’t an option for 120V. Mar 29 '21 at 3:40

Normal 120/240V residential power in North America comes from a center-tapped 240V single phase transformer secondary - the centre tap is grounded and is the "Neutral" connection. No need for your complex clalculations to prove that you can get 240 V.

You can safely connect your 240 V motor to the two 120 V "hot" wires.

• Really thank you Peter. These calculations are not complex. I just wanted to see mathematically..
– NIN
Mar 29 '21 at 1:25
• Peter: In the inverse way will it work too ? I mean : for example a dryer with tree connections (L1 - L2 - N ) will work if I connect L1 = 220 Vac ; N = Neutral ; and L2 = free ?
– NIN
Mar 29 '21 at 1:31
• No - for 220 V, you connect between L1 and L2 (between the opposite ends of the 240 V secondary). Dryers and stoves often need 120 V for controls and lights, so they also need a connection to Neutral. Mar 29 '21 at 1:38
• Oops... I edited the wrong thing Peter. Please feel free to reject my edit ;-) Mar 29 '21 at 1:38
• @Peter thank you. But I dont understand you very well. . . Let's suppose we have a motor which must be connected in this way : L1 = 120 VAC ; L2 = 120VAC (180 degree out of phase) ; N = Neutral. . . . But I live in a country which I just have two wires : 240VAC and neutral . . How could I connect that motor in that country ?
– NIN
Mar 29 '21 at 2:13