Difference between revisions of "Calculate Impedance"

[[Category: Physics]]

#Define impedance. Impedance is represented with the symbol Z and measured in Ohms (Ω). You can measure the impedance of any electrical circuit or component. The result will tell you how much the circuit resists the flow of electrons (the current). There are two different effects that slow the current, both of which contribute to the impedance:<ref name="rf1">http://www.allaboutcircuits.com/vol_2/chpt_5/1.html</ref>

#Review resistance. Resistance is a fundamental concept in the study of electricity. You'll see it most often in ''Ohm's law'': ΔV = I * R.<ref name="rf2">http://www.physicsclassroom.com/class/circuits/Lesson-3/Ohm-s-Law</ref> This equation lets you calculate any of these values if you know the other two. For instance, to calculate resistance, write the formula as '''R = ΔV / I'''. You can also [[Measure-Resistance|measure resistance]] easily, using a multimeter.

#*Inductive reactance X_L is produced by inductors, also called coils or reactors. These components create a magnetic field that opposes the directional changes in an AC circuit.<ref name="rf3">http://www.electronics-tutorials.ws/accircuits/ac-inductance.html</ref> The faster the direction changes, the greater the inductive reactance.

#*Capacative reactance X_C is produced by capacitors, which store an electrical charge. As current flow in an AC circuit changes direction, the capacitor charge and discharges repeatedly. The more time the capacitor has to charge, the more it opposes the current.<ref name="rf4">http://www.learnabout-electronics.org/ac_theory/reactance62.php</ref> Because of this, the faster the direction changes, the lower the capacitive reactance.

#Calculate inductive reactance. As described above, inductive reactance increases with the rate of change in the current direction, or the ''frequency'' of the circuit. This frequency is represented by the symbol ƒ, and is measured in Hertz (Hz). The full formula for calculating inductive reactance is '''X_L = 2πƒL''', where L is the ''inductance'' measured in Henries (H).<ref name="rf5">http://www.learnabout-electronics.org/ac_theory/reactance61.php</ref>

#*The inductance L depends on the characteristics of the inductor, such as the number of its coils.<ref name="rf6">http://www.learnabout-electronics.org/ac_theory/inductors02.php#backemf</ref> It is possible to [[Measure-Inductance|measure the inductance]] directly as well.

#*If you're familiar with the unit circle, picture an AC current represented with this circle, with one full rotation of 2π radians representing one cycle. If you multiply this by ƒ measured in Hertz (units per second), you get a result in radians per second. This is the circuit's ''angular velocity'', and can be written as a lower-case omega ω. You might see the formula for inductive reactance written as X_L=ωL<ref name="rf7">http://www.allaboutcircuits.com/vol_2/chpt_3/2.html</ref>

#Calculate capacitive reactance. This formula is similar to the formula for inductive reactance, except capacitive reactance is ''inversely'' proportional to the frequency. Capacative reactance '''X_C = ¹ / _2πƒC'''.<ref name="rf4" /> C is the capacitance of the capacitor, measured in Farads (F).

#Add resistances in the same circuit. Total impedance is simple if the circuit has several resistors, but no inductors or capacitors. First, measure the resistance across each resistor (or any component with resistance), or refer to the circuit diagram for the labeled resistance in ohms (Ω). Combine these according to how the components are connected:<ref name="rf8">http://physics.bu.edu/py106/notes/Circuits.html</ref>

#Add similar reactance values in the same circuit. If there are only inductors in the circuit, or only capacitors, the total impedance is the same as the total reactance. Calculate it as follows:<ref name="rf9">http://www.wilsonware.com/electronics/capacitive_reactance.htm</ref>

#Subtract inductive and capacitive reactance to get total reactance. Because one of these effects increases as the other decreases, these tend to cancel each other out. To find the total effect, subtract the smaller one from the larger.<ref name="rf10">http://artsites.ucsc.edu/ems/music/tech_background/z/impedance.html</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 = √(R² + X²)'''.<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 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>