Resistance (R) is the slowing of current due to effects of the material and shape of the component. This effect is largest in resistors, but all components have at least a little resistance. Reactance (X) is the slowing of current due to electric and magnetic fields opposing changes in the current or voltage. This is most significant for capacitors and inductors.
ΔV is the voltage, measured in Volts (V). It is also called the potential difference. I is the current, measured in Amperes (A). R is the resistance, measured in Ohms (Ω).
ΔV is the voltage, measured in Volts (V). It is also called the potential difference. I is the current, measured in Amperes (A). R is the resistance, measured in Ohms (Ω).
Inductive reactance XL is produced by inductors, also called coils or reactors. These components create a magnetic field that opposes the directional changes in an AC circuit. [3] X Research source The faster the direction changes, the greater the inductive reactance. Capacitive reactance XC is produced by capacitors, which store an electrical charge. As current flows 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. [4] X Research source Because of this, the faster the direction changes, the lower the capacitive reactance.
The inductance L depends on the characteristics of the inductor, such as the number of its coils. [6] X Research source It is possible to 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 XL=ωL[7] X Research source
The inductance L depends on the characteristics of the inductor, such as the number of its coils. [6] X Research source It is possible to 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 XL=ωL[7] X Research source
You can measure capacitance using a multimeter and some basic calculations. As explained above, this can be written as 1 / ωC.
You can measure capacitance using a multimeter and some basic calculations. As explained above, this can be written as 1 / ωC.
Resistors in series (connected end to end along one wire) can be added together. The total resistance R = R1 + R2 + R3. . . Resistors in parallel (each on a different wire that connects to the same circuit) are added as their reciprocals. To find the total resistance R, solve the equation 1/R = 1 / R1 + 1 / R2 + 1 / R3 . . .
Inductors in series: Xtotal = XL1 + XL2 + . . . Capacitors in series: Ctotal = XC1 + XC2 + . . . Inductors in parallel: Xtotal = 1 / (1/XL1 + 1/XL2 . . . ) Capacitors in parallel: Ctotal = 1 / (1/XC1 + 1/XC2 . . . )
You will get the same result from the formula Xtotal = |XC - XL|
The mathematics behind this formula involves “phasors,” but it 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. [14] X Research source [15] X Research source
The mathematics behind this formula involves “phasors,” but it 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. [14] X Research source [15] X Research source
Z = R + jX, where j is the imaginary component: √(-1). Use j instead of i to avoid confusion with I for current. You cannot combine the two numbers. For example, an impedance might be expressed as 60Ω + j120Ω. If you have two circuits like this one in series, you can add the real and imaginary components together separately. For example, if Z1 = 60Ω + j120Ω and is in series with a resistor with Z2 = 20Ω, then Ztotal = 80Ω + j120Ω.
