Difference between revisions of "Calculate Impedance"
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#*You will get the same result from the formula X<sub>total</sub> = |X<sub>C</sub> - X<sub>L</sub>| | #*You will get the same result from the formula X<sub>total</sub> = |X<sub>C</sub> - X<sub>L</sub>| | ||
#Calculate impedance from resistance and reactance in series. You can't just add the two together, because the two values are "out of phase." This means that both values change over time as part of the AC cycle, but reach their peaks at different times.<ref name="rf1" /> Fortunately, if all of the components are in series (i.e. there is only one wire), we can use the simple formula '''Z = √(R<sup>2</sup> + X<sup>2</sup>)'''.<ref name="rf11">https://www.nde-ed.org/GeneralResources/Formula/ECFormula/Impedance/ECImpedance.htm</ref> | #Calculate impedance from resistance and reactance in series. You can't just add the two together, because the two values are "out of phase." This means that both values change over time as part of the AC cycle, but reach their peaks at different times.<ref name="rf1" /> Fortunately, if all of the components are in series (i.e. there is only one wire), we can use the simple formula '''Z = √(R<sup>2</sup> + X<sup>2</sup>)'''.<ref name="rf11">https://www.nde-ed.org/GeneralResources/Formula/ECFormula/Impedance/ECImpedance.htm</ref> | ||
| − | #*The mathematics behind this formula involves "phasors," but it [[Use | + | #*The mathematics behind this formula involves "phasors," but it [[Use the Pythagorean Theorem|might seem familiar]] from geometry as well. It turns out we can represent the two components R and X as the legs of a right triangle, with the impedance Z as the hypotenuse.<ref name="rf3" /><ref name="rf12">http://www.learnabout-electronics.org/ac_theory/impedance71.php</ref> |
#Calculate impedance from resistance and reactance in parallel. This is actually a general way to express impedance, but it requires an understanding of complex numbers. This is the only way to calculate the total impedance of a circuit in parallel that includes both resistance and reactance. | #Calculate impedance from resistance and reactance in parallel. This is actually a general way to express impedance, but it requires an understanding of complex numbers. This is the only way to calculate the total impedance of a circuit in parallel that includes both resistance and reactance. | ||
#*Z = R + jX, where j is the imaginary component: √(-1). Use j instead of i to avoid confusion with I for current. | #*Z = R + jX, where j is the imaginary component: √(-1). Use j instead of i to avoid confusion with I for current. | ||
