Zed,

Welcome to ECN!!! (the Electrical-Contractor Network's forums).
Thanks for posting your questions, and I will try to answer them for you.

1:
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Can anyone explain how a capacitor provides a "second phase" in an electric motor.

Actually, the Capacitor "Assists" the "Auxiliary Winding" (AKA "Start Winding"), to achieve better starting characteristics on Single Phase "Split Phase" Induction Motors.

A typical 1Ø "Squirrel Cage Rotor" type Induction Motor will have a "Main" or "Run" Winding - and an "Auxiliary" or "Start" Winding.
The Start Winding is connected to the Motor's Circuitry via a Normally Closed Centrifugal Switch. This is known as the "Start Switch".
The Run Winding (or Windings), however, are not connected to any centrifugal switch, and remain connected throughout the entire operation of the Motor.

When the Motor's speed reaches aprox. 80% of the rated full speed, the Start Switch opens, and the Aux. Winding is no longer used. The Motor is now using only the Main / Run Winding for normal operation.
If the speed drops down below that 80%, the Start Winding will become active once again - until the speed reaches the 80% mark, when at this point, the Start Switch disengages - opening the Circuit to the Start Winding once again.

The reason for a Single Phase Induction Motor to include a Starting type Winding, is due to the "Non-Rotating" Magnetic Field of a 1Ø Circuit.
The 1Ø Field is stationary in space, but alternating in time.
Another way to view this is the sum of two equally and oppositely revolving Field Phasors.

Actually, the best description would be a "Semi-Visual/Mostly Imagination" scenario:
The Starting of the Motor would be similar to placing a 10 foot board on a fulcrum point at exactly 5 feet from either end, and placing exactly 10 Pounds of weight on each end.
The board just sits there stationary in space, because it is balanced at both ends.

To get the board to move, one side's weight must be reduced somehow.

If we remove 5 Pounds of weight from one end, the board will "fall" towards the end with the 10 Pounds of weight.
Now we have movement.

Take this analogy a bit farther, and imagine the fulcrum point is an Axle, which is 6 feet above the ground, and the ends of the board are 5 feet from the axle point (plus the weights are attached to the board's ends).
With 10 Pounds at each end, the board is stationary (doesn't move), because it is in a balanced state.

To get the board moving, we create an imbalance of weight by removing 1 or 2 Pounds from one end.
Now the board will begin to rotate towards the heavier side (or opposite from the reduced side).
The weight represents the magnetic field's intensity.

That is how the 1Ø Induction Motor is Started. The Start Winding "Reduces" the Magnetic Field of "One Side" of the Run Winding, which allows the Rotor to begin spinning.

Typically, the Motor is known as "Split Phase" - which refers to the Start Winding as an "Offset Phase" - split from the Main Winding.
The "Resistance-to-Reactance Percentage" between the Start and Run Windings is quite different.
The Start Winding is designed to have a much lower value, as opposed to the Run Winding - which creates a Phase Lead/Lag between the two Windings, and ultimately results in a reduction in the Field on one end of the Run Winding.

Motor Types - 1Ø Induction - Descriptions

A Motor with just the Start Winding used, is known as a "Split Phase Resistance Start" type Motor, and is adequate for large Fan type applications.

When more Starting Torque is needed, the addition of a Capacitor - in series with the Start Winding - is done. This gives a greater Phase offset, plus improved Starting Torque.
This is known as a "Split Phase Capacitor Start" type Motor, which typically gets used for Pump applications (like Air Compressors).

There are two variations of the Capacitor Motor described above.

One is the "Split Phase Capacitor Start-Run" type Motor, which uses a large value "Start" Capacitor to start the motor (up to the 80% speed point), and once that point is reached, a low value "Run" Capacitor is switched in to the Circuit - while the large value "Start" Capacitor is switched out of the Circuit.
The Aux. Winding is used throughout the Motor's operation - via one of the Capacitors.

The other type is known as the "Permanent Split-Capacitor" type Motor ("PSC" for short).
This Motor has the Aux. Winding connected 100% of the Motor's operation, via a very low value Capacitor. There is no Start Switch on these Motors.
Since these Motors have a low starting torque, they are commonly used on Ceiling Fans and Oscillating Fans.

Another type of Split Phase Induction Motor is a "Shaded Pole" type.
This Motor has no physically connected Aux. Winding - nor does it use a Capacitor or any switches.
The "Shaded Pole" is a short-circuited winding, which is wound "at an angle" to the main winding.
It performs the tasks of Starting by reducing the Field at a fixed end of the run winding.

BTW, Polyphase Motors - such as 2 Phase and 3 Phase types, are "Self Starting", and therefore do not require an auxiliary starting means.

2:

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I have also had a small electric motor that was low on power until we replaced the cap that was wired to it. How did the cap provide this extra power?

I can only assume this assisted with Starting Torque, or the Motor was either a PSC or "Capacitor Start/Run" type.

Here's a few Schematics of 1Ø Motors.
More may be found at the Technical Reference area under these topics (click on the underlined blue text to go to that page):

Schematics for 1Ø Motors - Series 1

Schematics for 1Ø Motors - Series 2

Schematics for 1Ø Motors - Series 3

Schematics for 1Ø Motors - Series 4

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Image 1: Split Phase Resistance Start Motor.
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Image 2: Split Phase Capacitor Start Motor.
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Image 3: Permanent Split Phase Motor.
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Good luck on the Motor studies!

Let us know if you have more questions!

Scott35

edits:
1: Found several spelling errors, and hope all were fixed!
2: Tried to clear up a few statements, and add more details to a few others.
3: Per the Schematics above, the numbers refer to notes found with the original posted items. See the Technical Reference area for details.

Me!

Mike (Trumpy):
I didn't know you had replied to this topic, until I submitted this one! (2 minutes apart!)
Talk about being on the same Hz!!!

[This message has been edited by Scott35 (edited 07-02-2005).]


Scott " 35 " Thompson
Just Say NO To Green Eggs And Ham!