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power factor

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stealthelectric

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Hi:
If asked to find the power factor - I know the formula to use is cosθ - but sometimes the answer is requires a minus sign in the cos - like cos-θ.
Is this to do with the direction of the sinusoids and/or whether one leads or lags the other. How do I know when to use the minus sign and when not to?

many thanks
 
The sign depends upon whether the circuit load is inductive or capacitive. For an inductive load the current lags the voltage. For a capacitive load the current leads the voltage. The phase sign is positive for an inductive load and negative for a capacitive load.
 
Do you know anything about complex numbers? This is where all that complex number rubbish you learned comes in.

A capacitor has an impedance of 1/jwC (where w is 2*pi*f). An inductor has an impedance of jwL.

If you multiply numerator and denominator (and Governator?) of 1/jwC by jwC, you get jwC/(-w^2C^2) = -j/wC - a negative imaginary impedance.

Naturally jwL is a positive imaginary impedance.

Drawing this on an Argand diagram, your resistance will span along the x axis (it has no +j or -j component = no imaginary impedance), your inductor impedance will span UP the y axis and your capacitive reactance will span DOWN (negatively) along the y axis.

This represents real and imaginary impedances pictorally which is much easier to look at. In the real world, if your imaginary power is too inductive (if you run a printing press with lots of inductive motors), you can add capacitors across the rail to cancel the +j component with some -j component. This is called power factor correction.

See - this stuff they teach you at school does have some real world applications.

Sorry for the lecture, but I feel better now

Let me know if you need it explaining more (or waking up)
 
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