When talking about AC power, some of the power consumed doesn’t actually produce real work. It gets used in the generation of magnetic fields and charges in inductors and capacitors.
The power being used in an AC system can be simplified by using a right triangle. The x axis is the real power being used by resistive parts of the circuit (in kilowatts, KW). The y axis is reactive power, that is power being used to maintain magnetic fields and charges (in kilovolt-amperes reactive, KVAR). And the hypotenuse is the total power used by the circuit, or KVA (kilovolt-amperes).
Literal side note: they’re all the same units, but the different sides of the triangle are named differently to differentiate in writing or conversation which side of the power triangle is being talked about. Also, AC generator ratings are given in KVA, so you need to know the total impedance of your loads you want to power and do a bit of trig to see if your generator can support your loads.
The reactive component of AC power is denoted by complex numbers when converting from polar coordinates to Cartesian.
Anyways, I almost deleted this because I figured your comment was a joke, but complex numbers and right triangles have real world applications. But power triangles are really just simplifications of circles. By that I mean phasors rotating in a complex plane, because AC power is a sine wave.
By that I mean phasors rotating in a complex plane, because AC power is a sine wave.
I read the entire thing as Air Conditioning and it made me think my tired ass had forgotten something important and then here comes like whiplash when it clicked that you were talking about Alternating Current.
Please be careful with two different things. Complex numbers have two components. Distances don’t. They are scalars. The length of the vector (0,1) is also 1. Just as a+bi will have the length sqrt(a^2 + b^2). You can also use polar coordinates for complex numbers. This way, you can see that i has length 1, which is the distance from 0.
The triangle in the example above adds a vector and a scalar value. You can only add two vectors: (1,0) + (0,1) which results in (1,1) with the proper length. Or you can calculate the length/distance (absolute values) of the complex numbers directly.
When talking about AC power, some of the power consumed doesn’t actually produce real work. It gets used in the generation of magnetic fields and charges in inductors and capacitors.
The power being used in an AC system can be simplified by using a right triangle. The x axis is the real power being used by resistive parts of the circuit (in kilowatts, KW). The y axis is reactive power, that is power being used to maintain magnetic fields and charges (in kilovolt-amperes reactive, KVAR). And the hypotenuse is the total power used by the circuit, or KVA (kilovolt-amperes).
Literal side note: they’re all the same units, but the different sides of the triangle are named differently to differentiate in writing or conversation which side of the power triangle is being talked about. Also, AC generator ratings are given in KVA, so you need to know the total impedance of your loads you want to power and do a bit of trig to see if your generator can support your loads.
The reactive component of AC power is denoted by complex numbers when converting from polar coordinates to Cartesian.
Anyways, I almost deleted this because I figured your comment was a joke, but complex numbers and right triangles have real world applications. But power triangles are really just simplifications of circles. By that I mean phasors rotating in a complex plane, because AC power is a sine wave.
I read the entire thing as Air Conditioning and it made me think my tired ass had forgotten something important and then here comes like whiplash when it clicked that you were talking about Alternating Current.
More coffee needed.
Please be careful with two different things. Complex numbers have two components. Distances don’t. They are scalars. The length of the vector
(0,1)is also1. Just asa+biwill have the lengthsqrt(a^2 + b^2). You can also use polar coordinates for complex numbers. This way, you can see thatihas length1, which is the distance from0.The triangle in the example above adds a vector and a scalar value. You can only add two vectors:
(1,0) + (0,1)which results in(1,1)with the proper length. Or you can calculate the length/distance (absolute values) of the complex numbers directly.Its another classic case of Euler’s Identity